The processor will be more then enough, but you will still get lag in Starcraft 2 when there's large combat. Just the same, Civlization V may lag once you are near the end of the game (or met up with other AI players.)
You'll get good framerate on high though.
Well, try it out. I never used a 4870, I'm basing off of my 5770 and Athlon which perform less then your setup.
With Civilization V, my CPU gets throttled after playing an hour. Your cpu should be better off for this, the same for Starcraft II but only in large fights like 4vs4 or higher where you may experiance lag with units attacking.