Yes you should be able to run source games but don't expect wonders, they will work but with all the graphic settings and eye candy turned off. You can grab a HD6570 for cheap ($50) and that will let you turn up the eye candy and get good frame rates. If you really want more eye candy then get yourself a better card. If you have a budget for it let us know
My neignbor works for AMD and says he can hook me up with a better card thanks for the input
Yes, source games are a little dated so you should have to problem playing it at pretty decent settings with that rig.