It is possible for sure, just don't expect to play the latest and greatest and max resolution and graphical settings. You can get a decent system for $400 though. Just hit up Newegg and look at some of their combo deals. They have some good stuff sometimes and you might even find an entire rig as a combo.
If you can wait for rebates, I would grab some higher quality parts that will give you a better build. Total is $455.79 including shipping. Minus $55 in rebates gets you to $400.79. You can dig between the cushions for that 79 cents