I doubt it. The first and foremost priority of a shipgirl is to keep her crew safe, not judge their actions.
To start, shipgirls are not in the chain of command. This means they don't give or take orders from anyone. This may change in the future, though, with two possible ways of going, depending on how the different Navies take the issue of shipgirls: basically, the brass designs aa new chain of command for the shipgirls, or they integrate them in the existing chain of command. Both have problems and advantages. This would also mean that the term "flagship" gains a very distinct and important meaning.
For hull-bound shipgirls, their world is the ship they represent, so the brass is "those guys that give orders to my Captain". In that case, giving different orders or assigning different duties to a shipgirl may undermine a Captain's authority, which is a serious issue. I'm not sure how it could be solved, except that both Captain and shipgirl attend jointly a briefing to receive orders and define clearly what is Captain's prerrogative, and what is shipgirl territory.
Hull-free shipgirls are another matter. They don't have a crew or even a Captain, their chain of command is totally internal when it comes to ship operation, so in that case it's important to have a seperate chain of command for giving or taking orders, as their level is only ship-level, which would mean that the human officer in charge of them has to be an Admiral or a fleet commander, regardless of rank.
This is an issue that hasn't yet been brought to the fore, but it will inevitably appear. With hull-bound shipgirls is not that important, because the physical ships are still operated by a human crew, so most of the time, they only need to know when to get out of the way. Hull-free shipgirls are their own captains, and this should be addressed now, with only Utah as a single example. But with the progress of the war, more and more shipgirls will become hull-free, specially if summoning of sunk shipgirls becomes a thing.
Which brings another interesting point: right now the only Navy that has an officer that knows that sunk shipgirls can be summoned back is the USN. That is a very critical piece of information, as it gives a serious advantage to the USN, so when the brass are aware of it, it will be classified in all the ways they can think.
