The only link between noble rank and government office in GT:Nobles is a list of positions with the minimum ranks required to fill them.
If we are both looking at the table on p71 titled Summary of Imperial Positions in GT:Nobles the table could present a model for precedence if no other exists.
I was also including the Lord Grand High Chamberlain (Hereditary office of the Archduke of Sol), the Chancellor of the Palace and the Majordomestic who is head of the Office of the Emperor (something close to the Keeper of the Privy Purse and Master of the Household).
Soc is probably too confining to use for everything, certain concepts, such as precedence, are most likely more evolved. T5 does break soc out more; but I think the precedence is about not letting a duke with title but no position, be able to give orders to a count with position, and that the fief is different than one's area of responsibility. One thing that is apparent, is that soc actually doesn't equal position, and that there is significant social mobility over the old orders of terrestrial nobility
Yes I think Soc and Precedence are quite widely separated both in real world terms and in Traveller terms. I think the dispersed nature of the Imperium is going to favor the person with the right skill set for a position rather than the proper breeding. Likely this is something that would be first to emerge in a spacefaring society followed by a system of peerage as it becomes a colonial society.