It should work fine. Your PSU is 350W and Dell usually doesn't use terrible PSUs, but you may want to check the amps available on the 12V rail. A decent 350W PSU should have at least 25A on the 12V rail(s) which is enough to drive a 95W CPU and a fairly powerful GPU.
However, gt640 is only 5670/6670 ddr5 territory at best. I mean you're looking at BARELY playable in BF3. I'd step up to a 7750 -- the lowest entry-level card I'd recommend-- which is going to be nearly two times as fast. I don't know your budget, but there are three cards on newegg for less than $100 after shipping and before rebates.