I know the answer to this question will start off with a well it depends but for those using gelatin while we are on the subject have you noticed a decreased hop character?
It can
destroy hop character, in my experience.
I recently did a northeast style apa (oats, wyeast 1318, loads of whirlpool and dry hops) that I split into two fermentors. I crashed and gelatin fined one and did nothing with the other and bottled. I took the resulting beers to a homebrew meeting and everyone was amazed at the dramatic reduction in hop flavor and aroma. The mouthfeel was noticeably thinner as well.
From that experience it is unlikely I will fine hoppy beers again.
It may be possible that certain yeasts, like Chico, don't grab onto as much of those precious hop oils, and thus would suffer less from fining, but I have no experience.