I have that exact setup (7870xt though) and yes you will notice some bottlenecking in CPU heavy games. It's not a huge bottleneck though, but may become more apparent over time as more and more games run better with a Quad Core chip.
I plan on going for an i5 soon but in no way will you need to rush on getting a quad.
My 7950 is bottlenecked but not a ton. Only about 5-10 fps. Yeah games are moving to quad core but i think you will be good with an i3. If it does bottleneck it will only be 1-3 frames. If you have the money go for a better cpu but if youre on a budget dont worry.
Disclaimer: none of the stats are proven or are being stated as facts. Just my guesses from my experience and research.