There was an entire TNG episode (Season 6, Episode 12) whose plot centered around this:
Moriarty was reactivated by mistake, and took the ship hostage, demanding to be able to leave the holodeck.
Geordi and Data spent half the episode experimenting with beaming (inanimate) holographic objects off the holodeck, to no avail. With that said:
Their transporter turned out to be a holographic fake (and so was Geordi), so who knows if the results were valid.
Nah, the SWAT would have to arrest themselves.
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.
A few thousand years later, Ed decides to create 20 18 superhuman clones of himself, and things start to get pretty grimdark.
I think you’ll find the holodeck is the cause of (and occasionally the solution to) most Trek problems.
Also the recent SNW crossover where she >!is thirsting over young Spock!<.
The EMH is never shown with pips on Voyager. The “ECH” was shown with pips appearing on its first appearance, however:
spoiler
The entire ECH subroutine was created as the result of The Doctor’s daydreaming, so the visualisation of a rank appearing out of thin air makes sense in that context.
The only other time the ECH mode was used in a genuine emergency (Season 7, Episodes 16/17), he did not have pips.