It can't hurt to ask, but some BO's are good about it, some aren't. I helped a student find her horse when she was ready to get her own, but since I didn't have any room left, I suggested a barn close by for her to board at. I knew the BO, had sent her boarding business for years. When my student took her horse there, the VERY FIRST THING out of the BO's mouth was, "you realize your instructor WILL NOT be allowed to come here to teach you or to help train the horse". No reason was ever given, but I suspect she wanted to railroad the poor girl into taking lessons from her instead. Needless to say, that was the last business I sent her way.
"Keep a leg on each side and your mind in the middle"