Go to www.dell.com, support link. Do a search for drivers using your service tag. See any Windows 7 drivers there? If yes, you are good to go, if not, it may not work. The way you'd find out is to install it, and see what happens. Generally the only issues would be with audio and video drivers, but that can be gotten around by buying a new sound and/or video card.
That system comes with several different CPUs, but a faster P4 in the 2.6+ gig range will run Windows 7 pretty well.