I'd guess that it all depends on how the Imperium's government actually works, as well.
I mean, we've been told that it is a form of feudalism, but I'm not so sure.
Feudalism is a system for structuring society around relationships derived from the holding of land in exchange for service or labor. But what land do the Imperial nobles hold and control? entire member worlds?
That'd make ALL member worlds to be gov-6, except they are not. Else nobles are representatives of the Emperor, whereupon they would be assigned to a member world in a manner similar to diplomats, but with some level of governing power.
In the first case, their troops would be the world's troops which could be ordered to fight for whatever cause the noble wishes, which would naturally be whatever cause the noble's lord wishes.
In the second case, the noble's troops would be ceremonial and/or security for the noble and his assigned estate.
Besides,
Feudalism traditionally emerges as a result of the decentralization of an empire. This was particularly the case within the Japanese and Carolingian (European) empires which both lacked the bureaucratic infrastructure necessary to support cavalry without the ability to allocate land to these mounted troops. Mounted soldiers began to secure a system of hereditary rule over their allocated land and their power over the territory came to encompass the social, political, judicial, and economic spheres as well.
These acquired powers significantly reduced the presence of centralized power in these empires. Only when the infrastructure existed to maintain centralized power—as with the European monarchies—did Feudalism begin to yield to this new organized power and eventually disappear.
I'm sure the 'centralized power/Emperor/Moot' would not like that!
I'm certain the X-boat network was an attempt to provide an infrastructure to exercise centralized power, but it was also too slow to do so effectively over such long distances. I'd be willing to argue that this decentralization of the empire precipitated the total breakup during the Rebellion along domain borders resulting is numerous smaller 'empires' that fought each other.
I prefer the second proposal, myself.
The closest real-world analog to this that I can think of is the manner in which the Catholic Church held power during the late medieval through the renaissance.
Thus, IMTU....
The nobles would act in roles similar to the Cardinals and Bishops with other representatives scattered throughout the member worlds and would hold a great deal of influence over the nominally independent governments of the member worlds without being directly involved in governing. They would answer to their central leader, the Emperor, and would pass information on to the member world's leaders including diplomatic pressure over a wide range of issues.
They would appeal to the common populations and engage in cultural imperialism, etc, etc.
The noble estate would be handled much as the Vatican with the lands being officially Imperial property outside the jurisdiction of the member world's forces/police. Attacks upon such an estate is considered as attacks directly against the Imperium.
So, to me, the noble's forces would be the 'imperial army', which would be ceremonial/security troops similar to the Vatican's Swiss Guard, and not some huge multi-division army complete with armor, et al.
The army, being the silent partner in the scheme of things may want a bit of autonomy and independence from the navy. 
