I do know you don't have to have steam running at all to play D:OS.
You can (only in some cases, not in others), but according to Steam that would be illegal.
Correction, it would be a violation of the TOU/EULA.
EULA/TOU doesn't equate to law. It's the creators attempt to cover their backsides. As such, and given they're written predominantly by lawyers, they will basically cover themselves in any which way they can conceive of. It may seem restrictive, but that's just to ensure someone doesn't attempt to find a loophole they can wriggle through. Whether it's enforceable would depend upon the courts determination of it's legality.
