They do, at least my old one does. I don't see why it would be a problem since most of these units don't use the hard drive except as storage for shows - the OS and bootstrap are in ROM on the mainboard. You could try it, as long as you don't mind voiding any possible support on it.
I'm not sure if modding a TiVo goes against any rules here, so feel free to slap me on the wrist if it is.