In controlled airspace you've got to obtain permission for everything. So that does include orbiting on downwind as well.
As far as orbiting on downwind in uncontrolled airspace is concerned, well, I don't know the exact legal status. It may indeed be illegal because of the turn direction - but that would suggest that orbiting towards the runway would be legal. Which sounds like a bad idea to me.
On the other hand there are not all that many uncontrolled airfields that regularly have 737s on a straight-in ILS approach.