It's a fairly normal situation in a revolution or a civil war for there to be a provisional government set up in exile, or in liberated territory, and for this to be recognised by other countries as a legitimate government.

Of course such governments often get up the nose of other governments even when thye recognise them in some degree, and this has some advantages as a mark that of the provisional government is not just a puppet. The position of General de Gaulle during World War II is a case in point.

Such a provisional government could not be a front for the UN, still less for the USA. It would have to be Iraq controlled. The legality of recognising it, and letting it control any Iraq resources outside the control of Baghdad would be interesting, but I would think there are plenty of precedents for this kind of thing happening.

As for the extent to which it would have any democratic standing, that would be limited, but once again there are plenty of precedents. What democratic standing did George Washington have?