Not *legally*... although I doubt very much if there would be any practical repercussions. I've upgraded all 4 of my OS X machines with the same install disk through every version of OS X and I've never even got a nasty email from Apple.
AFAIK, if the original owner still has 10.0 or 10.1 installed on his computer, then you can't legally install it on yours... at least that's the rule of thumb for used software, you'd have to read the EULA to find out for sure.