It might, but it would be slow. I'm running Kubuntu on a machine ca 2002 or so. 1.1 GHz, 512 MB RAM and it runs acceptably well -- with a low-end graphics accelerator (without it, well, OpenOffice and some other apps are horribly slow).
As somebody else said, you might want to try a lighter-weight distro. I put Xubuntu on an old Win98 machine (500+ MHz, 256M RAM) and it runs reasonably. And with FAR better support for the WiFi card than the Win support that came with the card!
Thanks Sionnsar!