Its much easier for us to answer support issues when they are sent to support. Our support system alerts us and tracks the issues, while the Art Talk forum doesn't. Prompt support is very important to us and we work very hard to provide it. Our goal is to reply within the same day.
To answer your question, yes, when you mark a work as paid, the buyer will automatically be unflagged.
If they don't pay and so you don't unflag, then they can't bid on either your or anyone else's auctions again, so there is no need to hold off relisting.