Here in Connecticut, officials have been told by our state interscholastic sports governing body that once the coach, with no assistants, is ejected, the ejected coach has fifteen minutes to be replaced by a non-student over the age of eighteen. It is not the officials responsibility to check for proof of proper certification, we don't even ask. No replacement after fifteen minutes leads a forfeit by the team without a coach, even if they are leading in the game.
Never comes up in high school varsity or junior varsity games, but does occasionally come up in high school freshman games (especially the visiting team), or middle school games.