No, you'd have to give them the car, because the rightful owners are denied a car by you keeping it. But be careful, licensing doesn't fall under traditional ownership/theft rules.

Obligatory IANAL but... Pretty sure possession of stolen property isn't legal even if you paid for it.

If the deal appears to be too good then you can be charged with handling stolen goods, which is a loophole closer for people palming off stolen items to friends for almost nothing. If you pay what is considered a going rate for an item that turns out to be stolen you are most likely not breaking the law, though of course that doesn't mean the property is yours or that you would be compensated for it's removal from your ownership. Note this is relevant to UK law, no idea about other jurisdictions.