According to scriptures --- No way.. It is evident even from common sense ..
First of all, one who has renounced should not live in his native place. After he has renounced he has to start living in another place. How is that possible for a king?
A sage should leave his native land right after he has renounced. He should live far away from his own, like a thief just released from
jail (Maitreni Upanishad 115)
Secondly, he has to be on the move always, he is not allowed to stay in a particular place for around 8 months of a year. Only during the rainy season he is allowed stay in a particular place. Obviously such a lifestyle can't be followed by a king.
An ascetic shall wander alone for eight months;" says the Aruni (8),
"he shall keep a fixed residence during the entire rainy season or
during just two months of it."
Thirdly, a Sannyasi has renounced everything. He can't own anything. Even for securing food he has to beg. But on the other hand, a king will own so many things. He also can't go begging for food.
The things that a Sannyasi is allowed to carry/own are very few:
A pot, a drinking cup, a sling, a tripod, a pair of shoes, a patched
garment against the cold, a loincloth, a water strainer, a bathing
cloth, and an outer garment: an ascetic should avoid anything else
other than these
Laghu Sannyasa (21)
Let him sleep on a river bank or in a temple. Let him not afflict his
body with extremes of pleasure or of pain. Let him bathe, drink, and
cleanse himself with water that is purified. When he is praised let
him not rejoice, nor curse others when he is reviled.
A Sannyasi also can not have a sexual life which a king is allowed to have. Moreover, a Sannyasi can not indulge in several matters which are unavoidable for a king, for e.g law enforcement etc etc:
"An ascetic's mind is inevitably perturbed if he behaves with women
foolishly in these four ways. When his mind is perturbed he will
perish. "Craving, anger, falsehood, deceit, greed, delusion, likes and
dislikes, fine arts, the work of interpretation, desire, passion,
possessions,  egotism, selfishness, the practice of medicine, law
enforcement, atonement, travel abroad, and the use of mantras,
medicines, poisons, and blessings: all these are forbidden to him.
Practicing them will cause his downfall
Narada Parivrajaka. Upanishad.