just from my own experience from a good few years of road cars and rally cars, I have never seen belt damage on exposed belts - obviously it is possible and somewhere it will have happened. However ironically I have seen the results of a debris that got INSIDE a fitted cover We took the cover off to find reinforcing threads hanging out of the belt all the way round and had obviously been like it some time.
At least if the cover is off you will see any damage very quickly, rather than in 30K miles time when it's time to check the belt as in our case...
It's unlikely that a small stone or whatever will actually break the belt, it will punch a hole in it possibly, but if you see the damage you can do something about it..

I guess I'm saying it's unlikely to make much odds either way, but if anything does happen to the belt (including it goes slack or whatever) you will get to see it quickly with the cover off.