We know that it was possible to both transfer and make a backup copy (Voy: Living Witness) of Voyager's EMH, the only reason for the crew to not spin up multiple instances of the EMH was ostensibly due to some unspecified technological limitations they had while stranded on their own in the Delta Quadrant, presumably some kind of dedicated holographic development lab such as Jupiter Station which was originally responsible for deploying the initial copies of the EMH to the various Starfleet vessels using it.

Now, given that the EMH was successfully transferred back and forth to the Alpha Quadrant on more than one occasion it stands to reason that the possibility of creating a duplicate of the Voyager EMH should have been a simple matter. Especially given the inherent risks of transferring him back and forth and potentially losing him, let alone the valuable medical and tactical working knowledge he had acquired over the past several years it stands to reason that they would have at least wanted to back up, if not retain a functional copy of the Doctor for themselves to debrief rather than just simply sending back to Voyager with all the risks that entailed.

So now, assuming this was possible what would have happened to the timeline if Voyager's EMH had been able to leave a copy of itself behind when it returned to Voyager?