I did a single player mission with 6 x 4 ship of hornets and 3 x 4 ship of tomcats arriving at the CV.
Here is what I noticed. The AI does seem to stack sequentially in altitude (2000, 3000, 4000 etc). Neither marshall nor tower give the human player any direction so I just slotted in behind the flights at the next altitude which was 5000. Normally I get "305 established angles 5000 etc" which towers responds immediately "Signal is Charlie... etc...". With the "305 established call being automatic once you are within a couple miles of the CV. When I arrived after a couple of AI flights in the marshall stack and pattern I got no response so I assumed I did not have signal Charlie yet. I went around the marshall a couple times and then I eventually got the tower saying Signal is Charlie. I assume this is the AI tower waiting to call you down once the pattern is clear. I got this message ahead of two flights below me in the stack and so I descended through their altitudes. My flight also had the lowest fuel state. I am not sure if the AI takes in account fuel state when choosing the next flight to give Signal Charlie but it appears it did. I am also not sure if this is common for flights descend through other flights altitude bands to get to the initial. Maybe it is because it is all VFR and stack altitude isn't necessarily related to fuel state? I also noticed that the AI tower landed a number of the hornet flights before the last two tomcat flights. I am not sure if it fuel state or endurance is in the AI decision process to call down the next flight.
At the end the CV managed to land all the flights (36 aircraft) it in a pretty organized manner. It was pretty cool to watch in VR from the LSO station flights entering the break with additional flights overhead. I think it would help if we could hear the AI flight communicate with marshall, tower and the LSO although with all of that one freq it could get pretty cluttered. It would also help to have some clarification from ED (perhaps in the manual) what is SOP for player flights integrating with AI flights (particularly for marshall stack altitude) and order of precedence for signal charlie. It also looks like 4 aircraft is max the AI tower allows in the landing pattern and the next flight does not seem to commence until the #4 has landed. Not sure how it is done IRL.
Anyway those are just my observations.