From the info we have, it seems like they certainly had a level of autonomy that would allow Regret, for instance, to lead a military op to the Rubble (and for Truth to run the low-level smuggling operation to find humanity's colonies, or to build up the Hierophant fleet) but it seems like Truth was the only one who was doing major dealings of that nature. I suppose a lot of their derived power might be from what Ministers and Vice Ministers they have under their personal sway; Regret before he was a Hierarch was able to command crews to do his bidding as Vice Minister of Tranquility, for example. Maybe it was a matter of having certain Prophets and Sangheili at his personal command and basically having them say on paper they were doing other duties to make a ship or a fleet "disappear" off the books, as it were.