Yes it removes all the Game center achievements. I recommend you don't remove them from gamecenter. The gamecenter stats barely take any space on the phone.
i love achievements in games so i dont want absolutely remove them. however im also a completionist, and i hate games with glitched achievements. its a good thing that u can remove them then. on xbox live u can remove only games with 0 achievements unlocked. and what happens if i change iphone? the achievements are also stored online and not only locally on iphone right? and if i remove a game then i download it again? unlocked achievements re appears?