Can I play Steam games in Linux?
How well it runs on your computer is highly variable. The important thing is that you'll still be able to use your computer while you're waiting for windows to come. Alternatives to this if you absolutely need your games is just putting your old hard drive back into your new computer or keeping your old computer set up until you can purchase Windows 7.
Here is a screenshot of me running Left 4 Dead on low settings, windowed, 640x480 at 11fps. So yes, you can play steam games on linux.
Keep in mind that I have a 1.8ghz AMD processor that's at least 4 years old now, an 8600GT, 2 GB of ram and I'm running dual monitors at a combined resolution of 2560x1024 which will slow down games unless you shut one of them down while you're playing. You will probably get better results on your machine. Crossover for Linux will play games a lot better than Wine but it's $40 and probably not a great idea if you're trying to save up for Windows.
On the other hand DOSBox, zSnes, etc all have native versions for linux and older windows games will run pretty well in wine so it's a great time to revisit some classics.
I wasn't suggesting you replace Windows with Linux, just that it would make your computer usable while you saved up for Windows if you otherwise didn't have access to a Windows machine that could play games.