According to experts of the Church, who deal with it, yes and no regarding free will and possession. The body is possessed, not the soul. The persons body is considered to be controlled by the demon or demons while the soul of the person is suspended. But for possession to take place the person had to open themselves up to demonic influence under free will.
There really aren't any rules we can be certain about, agreed, and there is nothing to say a completely possessed person doesn't have periods where they seem more or less like themselves. But the demoniac who hung around the graveyard (Douay-Rheims which I chanced upon translates it way differently, monuments which I assume would be burying grounds), it sounds like from the way he lived and behaved, he was never free and very, very strong. Manic depressives or bi-polar people males mostly can display extraordinary strength when in the manic state. Makes you wonder, doesn't it? But then people in emergencies sometimes seem to be able to summon extraordinary strength to save a life (rarely but happens). The latter I wouldn't consider possessed by a devil but perhaps God or an angel grants them the strength or it has a totally "this-world" biological explanation.
Anyway, that one was possessed by Legion which meant countless (or one, they can lie but not to God/Jesus, a duly commissioned exorcist, or other in the name of Jesus Christ when commanded to tell the truth) and living the way he did, he may have never had any peace until Jesus came upon him, cast them all out, and the man was seen sitting and in his right mind.
Also the king in what is now Iraq (I'm not sure the ancient country) was condemned to live and eat as an animal for about seven years as a judgement.
My understanding is that demons have to obey perhaps a hierarchy with Satan at the top, may exercise some free will in the narrow confines of their "assignment" or state of being, but God has the ultimate control, and He allowed it then and allows it now.