It is appropriate? Sure, what is the harm? It is always nice to see one's work recognised and appreciated. Just keep it short, polite, and to the point.
Is it expected? Probably no. The staff is busy, and if your question wasn't anything out of the ordinary, they would probably forget you asked soon.
Edit: mbert adds in the comments some interesting inside information:
I am an assistant at my university and answer a lot of emails through a ticketing system. Our signature says something similar about replying. This is because when I answer an email, the ticket gets closed and marked done. If you answer to this email the ticket gets reopened and somebody needs to close it again. So I would suggest to answer with a short sentence but only if you are not emailing with a team that shares an email ( like staff@... or support@... )