If a player bets out of turn may the player that got bypassed by this action check then subsequently raise once action is back to that player?
As always, rules may vary by cardroom, but generally yes. The common rule is that an out-of-turn action is binding if the intervening action does not change (whether that action is a check or call). If an intervening player raises, then the out-of-turn player is off the hook and may take any action.
So in your scenario, player 1 checks, player 2 is silent while player 3 bets out of turn, player 2 can either object that it is his turn and make an action of his own, or he can simply check, in which case player 3's bet stands, and players 1 and 2 are perfectly entitled to raise when the action gets back to them.