In ASA and NFHS, yes they can, but not in the same inning.
True- with exceptions! In the event of an injury or disqualification, if no substitutes are available the player that was a courtesy runner may enter as a sub in the same inning.
Other than that, a player that has been used as a courtesy runner may be used as a substitute later in the game. That player is subject to all of the usual substitution rules covering any other player on the bench regarding re-entry rights, her spot in the batting order, etc.
One caveat...I've seen people get confused when using the term "pinch runner". While we all generally understand that to mean "someone who comes off the bench to run the bases for another player", from a rules standpoint the term is meaningless. Such a player coming off the bench is either a courtesy runner or a substitute and subject to the rules covering those two separate designations.