well depends on what you mean by possible. although there is no evidence that demons do exist, and there are surely no reason to believe in them, thus there is no reason to believe you can be possessed, the word "possible" changes everything. for instance is it possible for them to exist? not that they do but is it possible that they could exist and could possess? thats really hard to say because we are talking about something that might as well be fiction, belonging to another dimension already makes it easy to explain a demon that follows the laws of another realm. im going to lean with no, simply as there is no reason to consider it there being no evidence to even allow us to suspect it or come up with the possibility in the first place.

You cannot be possessed by something that does not exist.

What the heck there is no such thing as a demon, unless you are watching True Blood then they are true

Demonic possession only happens in horror movies and it should stay there.