As both licences have the same number and there is no identification on any additional validity pages making them transferable, it is fair to assume that the EASA licence keeps the other current as they are both National Licences held on the same database at the CAA. There is nothing published on the subject so I have always maintained both at the same time, but I see no reason to assume any aditional test would be required if one had not been signed. A signature would be required to exercise the privileges and haveing made the effort to obtain both, I am surprised that the holder would not keep both signed up to avoid any confusion.
If the EASA licence was issued by another NAA then that would be a different case.