Several agents have requested my full ms, and one of them recently sent me a very kind no. She clearly gave the book a thoughtful, thorough read and her letter to me included encouraging and constructive feedback. I'd like to send her a thank-you note, acknowledging her time and encouragement. Is this appropriate? Or would an agent just think it was weird to receive a thank-you for what was, after all, a no?
If the agent went through all that trouble, you can do it, but it is a pointless exercise for the most part. We do occasionally get thank you's, oddly enough for queries, and they're pointless and we just throw them out. But for what she did, it wouldn't hurt, certainly, if you send something else to that agent sometime in the near future.
In all other situations I would not recommend the waste of paper and postage.