It will all depend on the show staff. I suggest addressing it to the stage manager or company manager (you don't necessarily need to get their names, just putting either of those with the show name will work). Whoever handles mail there (normally someone on the box office staff if you send it to the theatre itself) will pass it along to the appropriate person. From there it's all up to how they are feeling.
For what it's worth, as a stage manager I'll typically try to get Playbills requests back as long as they include a self-addressed, self-stamped return envelope. However, sometimes they do fall through the cracks, especially if they happen to come at a time when I'm swamped with show related matters.