Are players allowed to sit out during tournaments?

Yes. Sitting out (essentially folding every hand) is a legal tactic in both real money and play money poker. 

Think of it this way: After a tournament has started, a player cannot decide to pick up their chips and leave. Similarly, we cannot decide to arbitrarily remove a player and their chips from a tournament once it has started. All chips at the start of a tournament must also be at the final table in order for the game to be fair to everyone. 

A player who is sitting out actually puts his opponents at a significant advantage. The player who is sitting out is still forced to pay his blinds and antes, and is never able to build his stack. It's best to think of a player who is sitting out as simply folding every hand. This is a completely legal tactic, as it is up to any individual player to decide his own best strategy. For this reason, almost every online poker room allows entrants to sit out indefinitely during a tournament.

We do what we can to discourage this sort of behavior, but once a player has paid their entry, they are entitled to play their chips any way they like within the rules of the game.