We've all seen that squirrel vs carbon fork picture, haven't we?
If you've got a sensible number of spokes that probably won't happen, so it probably comes down to whether you lose control from a sudden steering deflection or skid on the freshly splatted guts.
I doubt anything fleshy is going to do well after being run over by a 100PSI road tyre, assuming a direct hit. TBH, the rabbits that don't have a sensible diving-for-cover instinct tend to be the ones that look rather unwell to begin with. Pheasants, OTOH, are suicidally stupid and I trust them even less than I trust plastic bags.
I had three Pheasants jump out of a Fenland ditch in front of me. Instead of heading across the open fen, the daft sods went straight across the road. Very twitchy ar$e time.
The one thing that really needs to get brought out here is man vs bee.
I had a recent experience on the carbon frame rocket of being about 3km from home doing about 20-22mph when I saw a haze on the road. As I got closer it resolved itself, too late by far, into a swarm of bees. 20mph man vs bee impact is not insubstantial, but after the impact damage you then have the 20 or so bees clinging to your jersey, shorts, leg hair, socks, shoes. I took at least three or four stings on one leg before swiping and swatting the little bast@rds off me, as I waved and waggled across the road. White van man coming the other way looked more surprised than I was.