Probably. Of course since it consumes a significant amount of power the stability of your system will depend on the quality of your PSU. I wouldn't expect that PSU to explode or anything though as the PSUs in the XPS machines a usually better than average. I say just get it and then run some tests to stress the system, like Crysis or by running Prim95 and Furmark at the same time. If you hear any strange noises comming from your PSU, then it's being stressed out and you should replace it ASAP. If you just get some stability issues after running those tests for a while then you should consider getting a PSU if you intend to leave it on for long periods of time.
Any spec on the psu?
^+1 It can handle upto HD 4850...
Been running an overclocked 8800GTS 640 for 2.5 years