Even without an official rank, on Voyager he was still considered a Department Head and (more importantly) the CMO, which gave significant authority (even exceeding the Captain on certain medical matters), regardless of whether or not he was ever given any pips. The same thing would likely apply on subsequent postings.
If he ever had to be assigned a rank for clerical/administrative purposes, it would probably be the default required rank for a Starfleet CMO candidate for the class of ship he was serving on.
Nah, the SWAT would have to arrest themselves.