Covert spy: Not a hostile unless they attack the party in some fashion. Would definitely benefit from party auras.
Invisible Enemy: Yes, definitely a hostile with some situational caveats that would be roleplay specific.
So the spy is a covert hostile that is not attacking your party right now. Perhaps he has some agenda, maybe the mission is to observe and report. It doesn't matter. The spy wouldn't be covert if they hadn't tricked you into taking them along.
In fact, in most of my campaigns I have at least 2 party members who are subtly if not openly hostile to each other thanks to the lack of cohesion on alignment. They still aren't hostile targets. The spy would fit under this category as well. Your party thinks he/she is a group member, and thus any spells cast would take this member into consideration as a friendly.
An invisible enemy
Hostile. Always hostile. It says it in the name: An enemy.
If you're talking more about being invisible, then an invisible creature not engaging in a hostile act would be neutral.
However, an invisible creature likely or considering engaging in a hostile act (Invisible Stalker) would be hostile. Even if the stalker didn't engage, it would still be considered a hostile because the intent could have been to stalk and then kill a player. The stalking alone is hostile intent, unless blatantly stated otherwise.
This comes with a caveat of obvious role playing. For example, a sleeping stalker could be considered neutral for the purposes of determining hostility. Other roleplay examples include invisible creatures just following players to observe out of curiosity. This wouldn't mean they are invisible enemies though. Even if you have a murderhobo group that considers grass a favoured enemy, creatures not hindering, attacking or being openly hostile wouldn't qualify.