Playing League without a 1:1 mouse?

Is it possible to play league at a competitive level without an optimum mouse?

I tried playing with a wireless mouse (those logitech ones) and it's just spirals outward when I try making a perfect circle movement with my mouse. Obviously it's not 1:1 ratio (cursor-mouse movement) but is it possible to play skillfully like that? (scanning the map, repositioning, landing skillshots would seem like a pain with all that acceleration)

P.S: I currently play with a Razer Deathadder, I'm asking because my friend plays with a wireless mouse and it was really sensitive. He's still pretty new and he likes playing champions like Ashe, which requires lots of attentiveness to your skillshots and positioning.