It does, to some degree
NOTE: i used another mod as example, since it was the most recent event for me, but since its a common mod on many packs (disable companions complaints), it should not be that different. If anyone knows otherwise, please correct me.
what it does is that out of the 3 reasons that balance how happy they are overall, the "choice of companions" is always positive. members will still try to leave if you retreat/lose too many battles or do stuff that they dont like, like pillaging.
i once had all companions in my army, the redwood pissed me off and went on a pillaging rampage ( i looter every single village they own 10+) in a row. by the time i finished Zaira wanted to leave because she was downright appaled at me and my leadership.
so as long as you dont cross the line, you should be able to keep all of them no problem (you also have the option to pay them, or just let them go and get them back, they are always available to rehire)