Your PSU is fine. It's won't impact your gaming. Worst case a very poor psu might crash the game or incinerate the computer, but no FPS change (:
I think you misinterpreted the question a little bit.
The OP is asking if they will need a new psu if they upgrade their cpu and if that cpu will increase fps at all.
That psu will be perfectly fine if you upgrade.
As to if it will help with gaining fps will depend on what game i believe, how ever piledriver is much better optimized compared to bulldozer so you will see some improvements across the board.
Also if you want to save a few bucks get the FX8320, it is basically the same except for a multiplier increase which can be easily changed in the bios.