it might bounce up inside the compartment somewhere, I just don't see this happening, you would need to hit it so it bounces and by that I mean it would have to hop up and get hit by the underside somewhere which would back it deflect back to the road and bounce back up into some "pocket" area under the car.
If it crawled up in there, parked, it could just crawl back out. Cats loose there tails this way

I know people!
But if a wheel hit it most likely it wouls smoosh. I have hit something a tad larger than a squirrel and it thumpity thumps neumerous times along the bottom of my car, I tried to slow down but it was night time and I was doing 55 65 on the highway, Georgia ! so I doubt I was going faster.... But it indeed rolled alot and ping ponged between the road and the bottom of my car and I saw it still rolling out the back

poor thing! No Smell! No Sticky!
I have had a plastic bag stick to my cat(ilitic) converter now THAT SMELLED! for months until it all burned off! I cannot imagine and animal not moving fast enough from a heat soruce to stick long enough for this to happen to them!
Birds have run into my grille in the past

thought I missed it.... I slowed and swerved! I could swear it went under and got away, didnt hear anything and never saw it, until a few weeks later and I was washing the car and the poor little thing was stuck in the grille all dead and dried, but I did not need to "scrape" anything! I just gently pulled it out