No, buddhas and bodhisattvas generally don't possess themselves, including righteous gods.
It is even more impossible to have a psychic fortune-telling or something.
It is rare for an old mage-Buddha and Bodhisattva to be possessed. Deciding when to possess is also a statement, and it is also a matter of concern for all beings. After that, you decided to leave and never come back. If you are often possessed, it is not a Buddha or a bodhisattva, but a demon.