"For they have sown the wind, and they shall reap the whirlwind."
I have to say, as a native auran, I get pretty tired of this kind of thing. There may come a day. You wizards. You think nothing of just summoning us across the cosmos, and you expect we're just going to do your bidding. One minute you're sitting around a garden in Aaqa shooting the breeze with your pals, or maybe you're out riding the winds, or even at home in a nice snug little cloud, and then poof, you're in some solid disgusting building in the material plane, and some clay-face material in a pointy hat is all saying do this, do that! And on top of that, the magic makes you have to be all friendly to it! I don't mind saying, I get a little claustrophobic! Have some empathy! I mean, what if the wind were blowing the other way? You don't think we have coercive magics? You don't think we have the conjure material spell? How cooperative would you feel?
- Windy, resident of the Plane of Air
Yes, the invisible stalker beats divination spells
Probably.
The invisible stalker entry does not say the mechanism of Faultless Tracker, and in particular it doesn't say it uses divination magic, so it is reasonable that the stalker beats nondetection, sequester, and private sanctum.
But you might need to check yourself
It's also worth noting that you the player have access in the Invisible Stalker stat block, you the character do not. While you may be a player character of true power and might, and can cast the spell to summon an invisible stalker, what you know about that creature you need to work out with the DM. A DM could very reasonably tell you you know the stories and the legends, but the only way to know for sure if an invisible stalker beats divination spells is personal experimentation.
Not so fast, though
You further ask:
Does this mean a summoner can summon a stalker, ask it to allow a spell being cast on it, cast telepathic bond on it to be able to communicate with it without requiring language, give it a quarry, and then telepathically ask it where that quarry is to learn their whereabouts?
Whoa. That's not a freebie.
The Invisible Stalker entry is actually pretty specific about how it works
From the text of the monster description:
An invisible stalker is an air elemental that has been summoned from its native plane and transformed by powerful magic. Its sole purpose is to hunt down creatures and retrieve objects for its summoner.
And:
Directed Hunter. When an invisible stalker is created, it stays at its summoner’s side until it is given a task to perform. If an assignment doesn’t involve hunting down and slaying a specific creature or recovering an object, the magic that created the invisible stalker ends and the elemental is released. Otherwise, it completes the task, then returns to its summoner for more commands, forced to serve until the magic that binds it expires.
It's not interested in playing patty cake. You give it a task, it goes and does it.
You're thinking, well, I'll word the task so that it will stick around so I can get my info first. Well, maybe. You can certainly try.
It has no reason to cooperate with you.
More from the description (emphasis added):
An invisible stalker is an unwilling servant at best. It resents any undertaking assigned to it. A mission that requires significant time might drive the invisible stalker to pervert the intent of a command unless it is worded carefully.
By default, I see zero reason for the invisible stalker to be interested in your telepathic bond, and zero reason for it to want to provide you with any information.
It arrived pretty annoyed with you. You have summoned it from its home. You have transformed it with powerful magic and bound it to your will. It resents what you're doing. It's reasonably intelligent and quite wise. Best case it's unwilling. Worst case, it's what, hostile? The spell doesn't say.
You're probably saying, but wait, conjure elemental says, "The elemental is friendly to you". That is in general. The specific case of the invisible stalker is governed by its statblock. In general a summoned elemental is forced to be friendly. The stalker is "unwilling at best" and "resents any undertaking assigned to it."
It may not be able to convey distance and direction perfectly
The stat block says it knows "the direction and distance to its quarry". I'm not sure it's a given that that is communicable. You seem to be assuming that that direction and distance is a numerical vector that the invisible stalker could communicate if it wanted. I don't think that's a given at all. Any hunter or even skeet shooter or for that matter baseball batter knows the direction and distance to its quarry, but they can't tell you numerically. I think it is far more reasonable that the "powerful magic" that transformed the elemental into the invisible stalker has given it a sort of hunter's sense of where its prey is, only on a planar level, than that it knows precise numbers. Find the path might be a worthwhile comparison.
How I would handle it as a DM
First of all, this is great. This is the sort of thing that makes the game truly fun. However, you, mighty wizard or druid, or whoever or are, are going to have to work at it every step of the way.
You get to know about invisible stalkers . . . a little
As a DM, by 11th level, I would give you for free1, that you have a general idea of what an invisible stalker is, and they feel confident they can summon one. They know invisible stalkers are unwilling servants at best. You would be at the cutting edge of your craft, not working from settled facts. Both the player and the character should be a little nervous, and the character's companions should be rolling their eyes a bit.
1 - Specifics dependent on the character: for a wizard, perhaps you've come across references in your research, for a druid, it was more likely passed down from your elders, etc.
The only way to find out if the stalker defeats divination magic is to try
Unless you find an incontrovertible source of in-game truth to the contrary, you just don't know if it's going to work.
What would your mother say
Summoning sentients from other planes is at best coercion. This really touches on what sort of game you're playing. The DMG gives as part of the description of the Plane of Air as "[o]ne such realm is fabled Aaqa, a shining domain of silver spires and verdant gardens...". You just snatched and compelled a resident from such a place. The stalker wasn't created by your spell, it was kidnapped. Maybe it's no big deal in your game, and that's fine, but it should be mentioned.
In a recent campaign we ended up deciding that summon elemental creates a spirit that had no prior existence and was made as your ally; whereas conjure elemental is actually ripping its elementals from their respective planes. Whether your invisible stalker is a pre-existing sentient is worthy of its own question, but that would be my ruling. The moral question should not be ignored. With great power comes great responsibility. However, war is hell, and if you're to save the world, you're going to end up with the blood of innocents on your hands.
The PC has to get the stalker to cooperate
Unless you have ways to compel or persuade it to cooperate, it flat out will not. Its goal is to get this over with. Maybe it would be willing to teach you a lesson if it can. Hopefully you didn't happen to dial up a fanatic, who's willing to die to fight back against this in-planar predation.
Let's assume you secure the stalker's cooperation
It flat out cannot give you perfect information. As mentioned above, my ruling would be that its knowledge is not in vector form. It's not using its eyes to see the target, it can't even point in the right direction -- what's it going to point with? Until the modern era, people thought of and conveyed distance and direction in very imprecise terms. And you're talking to a creature from another plane of existence. It's an air elemental, Jim, not a magical range finder. However, the stalker would be able to give you imperfect information.
You could keep trying
Conjure elemental lasts an hour. If you're looking for someone or something in this city, you might be able to get pretty close. Might take repeated attempts. That's gonna scale. You're not going to get the BBEG from across the world or whatever, with a single 6th level spell
In conclusion
Yes, the trick you describe probably works, both your title question and your actually more interesting in-text question. However, it is complex enough that no answer on the internet is going to be more than hypothetical. This scenario really requires the cooperation of the DM and the players to make the invisible stalker exploit a fun part of the game. I like it, and would love to play it or DM it.