What happens if you Ctrl+C, Ctrl+V on the Doctor’s data files? Do you duplicate a sentient being?
In “Virtuoso”, Tom & Harry try to reproduce the Doctor but they’re basically trying to make him from scratch, so I don’t think their failure is relevant.
At the end of “Author, Author” we see many repurposed EMH Mk1s working as miners:
…and they seem to be self-aware, so I guess we have to assume that it’s technically feasible.
But then what happens if you Ctrl+Z?
Basically, yeah, if you include all of their memories and experiences. The EMHs in the dilithium mines were EMH copies but weren’t The Doctor. I’ve also wondered if they were sentient or just good facsimiles. Part of The Doctor’s story arc was growing beyond his original EMH programming (plus B’Elanna expanding his matrix in some pretty hacky ways). So that leads me to believe that they weren’t sentient, though they had the potential to become so.
Anyway…
That said, the Doctor from “Living Witness” was, if I recall, the Backup EMH and had all of the The Doctor’s memories and was fully sentient as a result.
Essentially it would be the Will / Thomas Riker transporter accident equivalent for holographic beings.
VOY S5E11: Latent Image
they gave the convoluted explanation that emh doctor was more advanced than the ones in the mines and its hard to replicate his hologram programming.