What happens to the air in the engine bay would require either testing or simulation, as the shape of the car in that area is too complex to just wet a finger and figure out whether air flows in or out of the vents. Sure, air is going past the vents along the sides, but air is also speeding under the engine compartment. If the air under the car was static, yes I think air would probably flow out of the vents, the wrong way, but the air under the car isn't static.
Plus, these aren't simple smooth holes. That will affect things too.
The only one way to settle this is... ;0)
By the way, Bernoulli is always trotted out with this kind of stuff, with people saying air flowing over a curved surface (like the top of a wing) has to flow faster to keep from piling up air in front, and faster flowing air has lower pressure hence the wing experiences lift. Well, wings with mirror image curved top and bottom surfaces generate lift too, as do flat plate wings, so clearly Bernoulli needs a bit more explanation. The best way to look at it in my view is that if air is deflected through an angle (wings have an angle of attack) , it has had its momentum changed (momentum = mass*velocity - and remember velocity has a defined direction, so if the direction of the air is changed, the momentum has been changed so a force is generated as force = change in momentum.
Any time you change the direction of air, you generate a force.
Then there's the Coanda effect, but I feel that's enough for now ;0)