Time Machine by default does not run when no user is logged in. But that doesn't mean it can't. In fact, Time Machine is perfectly capable of running without a user logged in, but Mac OS X un-mounts all external drives -- including your Time Machine drive -- at logout. If you want Time Machine to continue backing up after you've logged out, it's as simple as setting your system to leave FireWire drives mounted after logout. You can find the instructions on how to do this in this hint.
I've also posted an installer package that will take care of it for you in my blog post on the matter.
[robg adds: I haven't tested this one.]
Mac OS X Hints