I would actually say that a F2P person can beat a P2W person, even if 1 in 5 chance or 1 in 10 chance in a Arena battle. If the F2P has a team that can counter the P2W person’s team then they may win, or at least in the Arena as Coliseum require that you spend on 15 characters when it is hard enough to keep up with 5 characters for a high leveled F2P player.
The best thing a F2P can do is to focus on counter characters, the best examples right now probably being Tron, Minnie and Timon and Pumba :-).
I have Tron good and working on Minnie right now, and after that probably Timon and Pumba maybe.