No. The check would be normal to hear, but it automatically fails to see.
I apologize for the magnitude of this post, but we need to understand a few things about...
Hiding in D&D
Hiding in English is to conceal from sight but hiding in D&D is both remaining unseen and unheard. Unseen Attackers and Targets
If you are hidden--both unseen and unheard--[...]
Bright light, no invisibility
If creature A was in bright light, and not invisible, creature A could not hide, since in Stealth,
You can't hide from a creature that can see you clearly[...]
Bright light, invisibility, not hiding
You generally know the location of an invisible creature that is not hiding since, Invisible condition
The creature's location can be detected by any noise it makes or any tracks it leaves.
But otherwise the creature is heavily obscured. Meaning, they aren't in heavy obscurity, they are heavily obscured.
An invisible creature is impossible to see without the aid of magic or a special sense. For the purpose of hiding, the creature is heavily obscured.
This means, without a spell, item or feature that allows you to see invisible creatures, you would be affected by the second bullet
Attack rolls against the creature have disadvantage, and the creature's attack rolls have advantage.
But you could otherwise "see" everything in their square, just not the creature as it is heavily obscured.
Bright light, invisibility, hiding
Everything applies as above, only, your passive Wisdom (Perception) or an active check must beat* the opponent's Dexterity (Stealth) check to hear the hidden opponent.
*: Tie in Contests
If the contest results in a tie, the situation remains the same as it was before the contest.
This is normally to the hider's advantage before combat, and to the seeker's advantage during combat, but not always.
It's important to note, there can be three or more types of Perception, the most common being seeing and hearing, but also common is smell.
Thus, on any given Perception check, you could succeed a Perception check and avoid Surprise, meaning, you
notice[.] a threat
Even if you could not see the creature, your successful check means you noticed it - and therefore know it's location.
What does it mean if I can hear (or smell) a creature but I can't see it?
It means they are not hidden and you know their location and if this was the start of combat you would not be surprised. However, it does not change the invisible condition and its traits, meaning the hider would still benefit from being an unseen attacker and target.
Why doesn't heavy obscurity have a penalty to Perception?
Light obscurity has a penalty, from Vision and Light
In a lightly obscured area, such as dim light, patchy fog, or moderate foliage, creatures have disadvantage on Wisdom (Perception) checks that rely on sight.
Note - the disadvantage is for checks that rely on sight. You have a chance to see, but not as good as if you were in bright light. This would not affect a Perception check to hear (or smell).
This also means the situation where you notice a creature, but cannot see them doesn't just apply to invisibility. For example, if a creature is hiding in light obscurity (say with Mask of the Wild), your Perception check to see them is at disadvantage, but not your chance to hear them.
But why doesn't heavy obscurity have a similar clause?
Because Perception checks that rely on sight in heavy obscurity automatically fail. This is far worse than disadvantage. You have no chance to see an invisible opponent without additional spells, abilities or features.
From Vision and Light
A creature effectively suffers from the blinded condition when trying to see something in that [heavily obscured] area.
And from Blinded
A blinded creature can't see and automatically fails any ability check that requires sight.
Effectively, the Wisdom (Perception) check (active or passive) against a creature in heavy obscurity is a Perception check to hear, only, and success would only mean you know their location. They are no longer hidden, but would still benefit from being an unseen attacker or target. Or hearing or smelling, in the case of something like a wolf.
Keen Hearing and Smell. The wolf has advantage on Wisdom (Perception) checks that rely on hearing or smell.
Without invisibility, you normally can't hide in bright light (see above) and in heavy obscurity, you have no chance to see, so most of the time, checks that rely on sight are made in the shadows (or other light obscurity), and at disadvantage.
Conditions to hide
Don't exist. They were in the playtest, but were left out of the official rules. I suspect this is because 5e makes no distinction between cover for an object or creature, so this would have made the lightfoot halfing's ability Naturally Stealthy worse than the conditions in the playtest. In the playtest, you could hide behind one-half cover, which is also any creature that blocks one half of your body. Naturally Stealthy allows a lightfoot halfing to hide behind a creature one size larger.
However, most have gleaned the conditions from the rules, but check with your DM as interpretations may vary.
You can't hide from a creature that can see you clearly[...]
if you come out of hiding and approach a creature, it usually sees you
It is generally understood that you cannot hide in light obscurity or bright light and generally not when already noticed, without a special ability like Mask of the Wild (in some light obscurity) or Naturally Stealthy (behind a medium or larger creature) or the Skulker feat (in light obscurity). But this is essentially reverse engineering a condition to hide that otherwise doesn't exist in the rules
You can't hide while being observed.
Or, more accurately
Hiding requires total cover or heavy obscurity
You need total cover or heavy obscurity to hide, unless you have a trait or feature that allows you to otherwise, but only light obscurity to remain hidden. This is also how hiding works at Keith Amman's table, demonstrated in his examples in his excellent book, Live to Tell the Tale.
Also, after reading Live to Tell the Tale, I now have the players roll a Stealth check each time an enemy has a chance to see them. They know this, so it obviates the need for hidden rolls to avoid meta-gaming on the hider's part.
Other senses that mimic sight (or hearing? or smell?)
Blindsight, Darkvision, Tremorsense and Truesight all impact darkness and all but Darkvision impact invisibility, however, it is not always spelled out how a particular sense works, so how a special sense that isn't described is affected by a Silence spell or a deafened creature is generally up to the DM.
Eldritch Invocation Devil's Sight donut hole
It's also important to note, darkness is dim light and dim light is bright light for creatures with darkvision, with the sole exception of a warlock without darkvision that takes the Devil’s Sight invocation. They see normally in bright light and darkness, but dim light is still light obscurity for them. Devil's (and warlocks with darkvision) don't have this limitation as they already have darkvision.