Very true. I don't think we've seen the E fire off a bunch of torpedoes in succession so I'm not sure how many the magazine would initially hold. My guess is at least 2 since in TSFS they got 2 off from the starboard launcher in rapid succession.
Which would make sense as during VI they fire one from each tube in sequence.
I got the impression that rather than the Enterprise being a "general purpose" training vessel, the purpose of the training mission specifically to train a new crew for the Enterprise. This is based on McCoy's comment to Kirk after the Kobayashi Maru simulation, "Admiral, wouldn't it just be easier to put an experienced crew back on the Enterprise" (or something to that effect).
They weren't training cadets to serve on other ships, they were training them to replace a previous crew. There is no need to assume that the Enterprise had been downgraded or taken off exploration assignments for good. She was still ship of the line, they just in the process of familiarizing her new crew with the ship and systems. Also, Kirk indicated he wanted to return to the Genesis Planet at the end of TWOK. Not a likely expectation if the Enterprise would only be doing training missions for the foreseeable future.
What is uncertain is what would have happened to the command staff once the crew was prepared for actual duty. Kirk had taken himself out of the equation. Spock didn't seem to want command outside of a teaching environment (of course he might have just been trying to encourage his friend assume command).
That is a good way of looking at it, I hadnt really thought of it that way as every assumption I had ever read was that the ship was now a training vessel. It makes more sense that they would be training a new crew of due to graduate Cadets and Trainees to crew a ship. That is echoed in ST2009 where the ships of Sol Fleet end up largely being staffed by Cadets.
Sulu seemed to have another assignment. It's entirely likely that a new commander would have been brought in.
Which depending on how you consider the novel and cut lines from the original script would be as Captain of Excelsior.