I don't think it would be all that worth it. The 3.1GHZ quad core is still capable. I don't think the bottle neck would be enough to even notice in game play using an HD 7850. Which MB do you have? What resolution is your monitor?
The problem with the Athlon II is lack of a L3 cache. Recent reviews shows that it severely hurts performance in newer titles. Hence why it was dropped off the list for best gaming CPU's for the money. If not for the better arch and faster clock, the 750k would also probably be on the list, as it suffers from the same issues, just to a lesser degree than the older Athlon II's. Older games you will be just fine. Newer titles have proven that it just isn't very capable anymore compared to other budget options out there. If your board supports it, an FX 6300 is a great CPU for the money.
I still don't think the HD 7850 would suffer all that much bottle neck from the Athlon II quad core. Not enough to make it a deal breaker. Replacing the CPU with something quicker would be OK, but that's why I asked about the MB and resolution. To see if it is cost effective... for a young person who gets his money from his parents.
I personally have used the Athlon II x4 635 for the past 3 years straight before upgrading to the 3570k and it stands up but barely. Even overclocked it bottlenecked even my GTX 460 and had huge fps drops in open world games. Its basically only good for older first person shooters, def replace. Im glad I did.