Proxima Centauri is a 20th of a light year from the main pair, ergo no real influence.
Well, not exactly -- it could have a positive influence. In our system, the Sun's heat burned off all the water in the inner system, and it was bombardment by comets from further out that restored water to the Earth. But Alpha Centauri A & B's respective gravity would've scattered any outer planets or comets (plus you've got the heat of two stars to evaporate volatiles), so if there were just the two stars, any planets around them might be bone-dry. However, assuming that Proxima Centauri actually orbits A & B rather than being an independent star that's just passing by (there's still some doubt about that), then its gravity could've sent comets from the system's Oort cloud inward to bombard the planets, so they could have water after all.
Although the flipside is that they'd still
be getting bombarded with comets periodically, which might hurt the chances of higher life or civilization evolving there.