It surely won't FULLY work because it lacks the right drivers. But with some luck you can download those from dell.com using your service tag and then it might work.
But just as well it will refuse to install (after checking the hardware) or will not run satisfactorily even after installing all drivers. Then you need to order the right recovery media with Dell. If they don't have those any more, you need to find a retail version of an OS to install.
Are you sure there is no recovery partition on the disk to reinstall the OS? That's a common way to spare the cost of a disk.
I have a inspiron 2650 and I need to reinstall windows from the dell CD, but I don't have the CD for this laptop.
I do have a windows reinstall cd for my dimension 2400 desktop.
would the windows reinstall cd that came with the desktop work on the laptop? xp home is on the cd, which I think is the version installed on the laptop.