The whispy connecting structures appear to be just that - connective structure.
Yet it connects two decidedly inhabited parts of the ship, and assuredly features a means of personnel access between the two - plus wantonly displays multiple rows of windows!
I thus see every reason to argue that this structure is inhabited, being no more awkwardly shaped for that than the saucer. This doesn't mean I wouldn't agree that the habitation functions there are afterthoughts and things shunted to an inoffensive and uncontested location. Most habitation functions in most human vehicles are! Placing all the unskilled and useless VIP passengers in there would be a fairly good solution from the practical point of view, too.
The TMP refit certainly seems to attempt to make the neck area more utilitarian, turning the windows into the smallest portholes anywhere on the ship, adding the torpedo launcher lump, and drawing in the hull detailing the suggestive vertical shape of, well, it was intended to be the warp core but it's in the wrong place due to the engineering interior set cock-ups. But that may simply indicate that Starfleet sacrificed former passenger spaces to accommodate new gear in old dimensions.