It might bottleneck it in some games but not at all in others. It does depend on the game and how CPU dependent it is. Battlefield 4 multiplayer (not single) will probably be bottlenecked as well as skyrim a little. If you have good cooling you can overclock your CPU. What's your CPU cooler?
If you do want to upgrade to a new motherboard/CPU the AMD 6300 and an AM3+ motherboard seems to be very good value. if you already have an AM3+ motherboard ou might be able to just upgrade you CPU. List your motherboard and i'll check to see what's compatible with it