As long as you're okay with accepting lower graphic settings for the newer games, go for it. Besides, with some of the money you save, you can use it to invest in a bigger, better GPU down the line. (Although, it might be overall better if you invested in some faster RAM; at least 1866. Depending on how good of RAM you get, you might experience upwards of 20% performance boost, for gaming.)
My significant other has a A10-5800K. She working on Mass Effect 2, going on 3, and they run perfectly fine. I recently bought her Tomb Raider, which will only get decent frame rates when I set most of the settings to low. (Texture quality, level of detail, and depth of field are still at medium.) It's not the enthusiasts' dream, but game is still playable and doesn't look completely awful. I am actually thinking of upgrading my own video card (Radeon HD 6870) and installing it on her computer.