It will be fine, but only for now. As games start using more and more cores, the bottleneck won't be the speed of your i3, it will be the fact that it only has 2 cores. That won't just be on the R9-270X, that will be on any card because it will be a CPU limitation that is not tied to graphics.
You don`t have to upgrade, your cpu is fine for now, you will need to upgrade it in the future, when you want and the cpu does not deliver enough performance for new games and you have enough money for a good quadcore cpu. Most games need a good GPU more than CPU anyway.