If Peter Griffin just holds on to the front of the
Falcon, I'm sure the
Enterprise could fly like that.
As much as I would like for it to, I just don't think engineering works in the primary hull. I think there is probably a small, one-level impulse engineering up there, which might be able to correspond with a small one-off set we've seen, or might be something that we haven't seen, perhaps along with engineering department offices as suggested in 'TMoST.' We might want to creatively reinterpret 'TMoST's references to engineering headquarters at the rear of the saucer meaning engineering headquarters for the saucer only.
But I think FJ's configuration for engineering just doesn't work. There isn't enough room for it to stretch as far as it does, with the saucer undercurve taken into account. If we pretend engineering is narrow, it might barely fit in the neck, but I really doubt it. I have never tried it, but I wonder how well the engineering set would fit if moved upward to allow ceiling clearance in the radiator-type element atop the saucer? Somehow, I don't think it wold work any better.
Oh, there are undoubtedly numerous "engineering spaces" in the primary hull. Just not "main engineering."
The real problem here, as far as I'm concerned, is a tendency for people to think of the ship in terms of "rooms." As if someone just came up with a cool shape, cut the inside up into volumes, then put the hardware into those rooms.
A "real" ship is designed in a very different manner. You build it from the inside out... almost opposite of what I think some folks are thinking here.
In other words... you start with the critical hardware, the critical routing, the critical mechanical structures to support all of that. THEN, once it's all in place, you start fitting control rooms and support facilities and storage spaces and, eventually, living spaces, around that.
So don't think of it so much as "rooms." It's not a flying hotel, it's a big machine which just happens to have pressurized spaces for people to work the machine (and repair the machine) from, and for those people to live when they're not operating it or repairing it.
I've said before, I don't care for the external layout of the Galaxy Class, but I LOVE the level of thought that went into making it "real" after that point. The idea of it being a huge spaceframe with habitable volume modules strung up throughout it as necessary makes great sense. I have no problem with the earlier-generation ships not taking that approach (and being "hard-structured") but I still think the idea of it being a machine first, and having the various spaces inside conforming to the machinery instead of vice-versa is by far a better idea.
That said...
Of COURSE there are engineering spaces in the P-hull. There will be engineering spaces for access to and control of the life-support and recycling systems in there. For access to and repair of the computer systems. For access to, repair and fueling of, and local control of the propulsive (including maneuvering) systems.
But none of those are the "main engineering" room. Main engineering is located close by the most critical systems in the main ship's hull. Undoubtedly, the propulsion control computer, the power-conversion systems, etc. Whether the power GENERATION occurs there or not is debatable, but that's almost trivial, I think. This facility isn't where you perform the main repairs on broken hardware, it's where you CONTROL the propulsion systems from and monitor their condition. So technically, this COULD be anywhere.
The only real hardware in "Main engineering" are the big transformer sets which seem to move around on the engineering set floor from show to show. I think those really are step-down transformers... but your mileage may vary.