It won't change any lag issues, but in a fair fight yeah, quicker is going to be better.
You need an adaptor to play on console. I got the XIM4 because the others are aimed more at the script kiddies and their cheats. It's nearly as expensive as your GPU though, (£133) so probably not worth it for you mate.
I picked up the XIM4, a Corsair K30 gaming keyboard, Logitech G502, a Sony navigator and a decent gaming mat, for £160, all boxed. I bought it for pc basically, as the XIM4 changes the setting profiles automatically from game to game. I'm only practising on PS4 before going and getting my [censored] handed to me on a plate on pc...