Of course it can be done.
But Everton would have to get everything - absolutely everything - right to get out of that division.
But you're looking at integrating/building an entire new squad (fine), maybe a new manager (we'll see on that), and the club never having in most of our lifetimes having been down in this position. We'd be facing a more congested season, which given our injury record isn't good news, and we'd be building the squad on very limited funds. That squad would somehow have to have enough quality to get promoted out of one of the toughest leagues in the world over 46 games.
Teams like Norwich and Fulham - they're set to come down and go back up because they keep the core of their squads together. It's why they don't have enough, usually, to stay up, but they know how to get back up.