A long time ago, when Traveller first came out, after I have gone through it and gotten a few issues of the JTAS, I wrote a letter to GDW asking how the Imperium compared in control to either the Roman Empire or the British Commonwealth. His response indicated that their thoughts were that it was somewhere in between: less control than the Roman Empire, partly due to the communications lag, but more than the British Commonwealth. The idea that I got was that a local world could develop in its own way, without be bothered too much by the Imperium, but if the equivalent of the Imperium governor-general, read Imperial noble, decided that intervention was necessary, he has a limited amount of immediate force that he could use, but he could call on considerable reinforcements if the matter was deemed serious enough. He, the monitoring Imperial noble, would have to give a detailed account of his actions to the Imperial Court. Depending on that, he might get advanced, might stay the same, or might find himself/herself in sitting on Yorbound, in charge of a research station testing resistance atmospheric suits.
Involving Aslan mercenaries within the Imperium should shift the Imperial interest to utter disinterest to intensely interested.