This documentation explains your options
You can upload listed or unlisted versions for any add-on you have on AMO. The suggestion of setting the add-on to Invisible is just so the existing listed versions aren't visible anymore, which is probably a necessary step if you want to move to unlisted.
As for the original question about moving users, listed add-ons aren't allowed to move users from a listed version to an unlisted one. It's okay to tell users about unlisted versions that are available, but it should be up to the users to actually make the switch.