No, not really. That CPU is too old, it has no discreet graphics or any capable graphics, so you would also need to purchase a gaming card as well, which would be severely bottlenecked by that old Core2 processor. Really, it is not feasible at all. For very low end games, if you bought a somewhat decent card, possibly, but realistically, there is not much in the gaming world you could do with that that makes any sense at all. You'd be much better off looking to some kind of newer prebuilt if that's the route you want to go.
Nothing older than an Ivy bridge or FX 8 core CPU should even be remotely considered for a gaming machine, even a low end one, and even those are so long in the tooth that you would almost immediately be looking to...