As a Romanian, I have to answer positively. Yes, it would have been possible, even if a stretch.
Had King Mihai I not angered the Soviets with his Royal Strike they might have kept him as a puppet. Stalin had King Mihai I in high regard and even had him decorated.
Let's say that if everything went smooth and King Mihai I was super compliant there would have been some 25% chance of him keeping the throne.
Of course, he might have been deposed later by the autochtonous communists (after the Red Army left the country).