They would miss having the right to perform weddings, I imagine...?
I doubt it. This is how it used to be in the UK years ago. The wedding was conducted at the KH and then the couple went to the Registrar's Office for the legal part, or as often happened at our KH, the Registrar came along to the KH, sat through the service and then did the signing of the register. We always had the same Registrar, she was a very pleasant lady and attended many JW marriages. She appears on many of our KH wedding photos, the only thing she insisted was that the register was covered for the photos.
George