Why not? This takes a few seconds of computer work, which the gate agent ought to do. It might also involve paging both customers to check in at the desk so they can be given proper boarding passes. This kind of thing happens all of the time. In fact, its part of the reason people have jobs to work at the gate and, thus far, those automatic gates have not been used outside of a few tests sites. There is not reason to not accommodate pax in this way.