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Yes, provided the rescuing Hero has access to the Site you can add that character to battle. That is the qualifying condition to turn it face up and remove it from where you've placed it.
Face Downcards are cards in territories, battle, and set aside areas that are face down either due to special ability, or are inactive artifacts in an artifact pile. Face down cards have no abilities, brigade, titles, or identifiers while they are face down. The only known attribute of a face down card is the card type. Face down cards are only targetable by abilities that specify they can target face down cards or inactive artifacts, or cards that can target any or all cards in a location. When a face down card enters battle, it is immediately flipped face up, unless otherwise specified by the special ability that flipped it face down.
Default Conditions* Placed cards remain where they are placed indefinitely.* Placed cards are placed face up.* Targets must be in play.
The default conditions for "Place" would indicate that the character would have to remain with the site until it is triggered by the ability (RA at site):QuoteDefault Conditions* Placed cards remain where they are placed indefinitely.* Placed cards are placed face up.* Targets must be in play.
Except the second point would seem to contraindicate this situation.
YMT is correct, and the default condition is that the placed card must remain unless something else acts to make it no longer placed. There is a reason why Tower of Thebez has to specify that you can return to territory; otherwise, you could not block with them.