No, I meant that in addition to upgrading your GPU, I suggest also buying a second 2GB RAM module.
Now, I will assume for a while that you run Windows Vista/7. Windows by itself will consume 700 MB-1GB of RAM at startup (mine consumes 1.3 GB, but I think that's because I now have 8GB RAM). Open a browser, that adds 50 MB. Open a game, that's easily 800 MB - 1.5 GB. You can see how fast your 2 GB of RAM will bottleneck your system. You will notice this when it comes to loading new areas, where the game will hang up for a second and smoothen out again. Your game load times will also take a hit while Windows is freeing up some memory for your game.
4 GB should be more than enough. Even with 20 browser tabs, a media player, and a game, you wouldn't be able to use all 4 GB.
So recap: It's OK if you don't upgrade the RAM, but I highly suggest you do. It'll help with system responsiveness even outside of games. The CPU you currently have is a good one, so I don't think we have a problem there. It might bottleneck since you're playing at 1600x900, but it'll give you smooth framerates with the 6870 even at high settings.