Excellent points Wingsley. allow me to explain my ideas point by point with yours.
1: My notion of the discarded secondary hull comes from a TOS episode, shamefully I don't remember the title, where the Enterprise was held by a tractor beam from planet side and Kirk told Scotty to jettison the warp nacelles and secondary hull and crack out of orbit with the main section. This also leads me to consider that the impulse engines are a good deal more powerful than they appear or the reduction in ships mass would give them an edge, the latter more likely than the former. This also leads me to believe that everything that is considered important is in the primary hull on the Connie class and the secondary hull is just additional storage/fuel/lab space and mounting for the warp nacelles. Given my line of thought, it would be unlikely that a secondary control room would be installed there.
2: As applied to TOS, it just makes sense to be able to overide the main bridge controls in an emergency situation. In TWK, kirk entered the Reliant's console prefix and dropped her shields, so it would be relatively simple to cut the main bridge console from a secondary location, given that you have the correct security codes to use in accomplishing this.
As far as an independently controllable secondary hull in TOS goes, I can't see it. Given that the Galaxy class is supposed to be the first ships in Starfleet service that can separate and rejoin the saucer and secondary hull and this is some 80 years after Kirks time, I just don't see the tech being there or even needed during the TOS era. Now during the movie era we did see the warp sled for Spock's shuttle and when the shuttle detached it appeared to turn and head back to, I assume, Vulcan. Taking this into account, there may have been a control room in the secondary hull of the Connies in the movie era, but the Connies were designed to only separate in an emergency situation, so to me this still seems a bit unlikely and very unlikely in the TOS era. Hope to hear from you and others again about this subject, this is an interesting topic.