I played Starcraft 2 on that same setup for a few months on low settings. The game is still really playable, but 2 GB RAM is really the bottlekneck here.
I had to restart my computer before and after SC2 because the system would become extremely slow while playing. After closing the game I could barely do anything either. Restarting (clearing the RAM) always fixed this.
But.....I bought 8 GB of RAM and my computer felt like a completely new computer. SC2 no longer slows my computer down and the game loads much much faster.
At first i thought 8 GB would be overkill, but IT IS NOT. I am consistently using around 4 GB of RAM and when SC2 plays I use over 5. If I had not gotten 8, I would have experienced the same slowness when the system needs to begin shuffling things out of RAM into the HDD.
Also, when I had 2GB, it was hard to have iTunes and other apps open because of limited amount of RAM. Now I can play, have iTunes open, adium open, Mail open, Safari open, and still have a ton of free space.
So yes, long story short, you can play games on that computer (WoW and SC2 and Warcraft III from experience) but be wary of the limited amount of RAM you have. It is hard to have many apps open at once when playing this games and your system may slow down after playing until you restart.
You should really consider upgrading your RAM to 8GB. 4 should be good if you cannot, but you will amazed how different the computer will feel if you can up it to 8.