While this is certainly a novel idea, it does raise some problems with the stability of the system, especially if Chaos tries to sabotage it. Compressing, storing and reigniting solar material makes a lot of sense. So while we don't need a "proper" Dyson sphere, there could be about a dozen "mini" Dyson spheres containing small, sun-like reactions.
Basically. But bigger.
While it is a novel idea, my first instinct would be "no" for a number of reasons.
1. Castle Heterodyne = AI = A big Mechanicus no-no
2. A centralized control unit is effectively impossible on a ship where it could take 12-14 minutes (8 light-minutes stem to stern times the speed of electricity along a coaxial cable) for a command to even reach where it's going even by electric signal.
3. If there's one thing the Mechanicus loves, it's redundant decentralization of systems and using cheap, replaceable human lives instead of precious, precious technology.
There is only one pilot, and He is the God-Captain, savior of All Mankind.
Also, there should be no FTL in The Ship. It takes away from the theme of it. Not to mention the difficulty manipulating the warp inside not only a Gellar Field but under the Emperor's Own Gaze.
And yes, it is heavily implied in the Horus Heresy novels that the Golden Throne basically sits atop a webway gate the Emperor was building, and the Custodes guard the gate just as much as they guard Him. HOWEVER, in the timeline of the ship, having even attempted webways within the ship goes against our previously established idea. The Emperor only woke up once, to order the construction of the ship. Period.
However, that's not to say some sneaky Eldar haven't been hiding aboard somewhere, or a Chaos cult has unlocked a ritual to that effect. But not the Imperials.