Yes and no
Yes, if there was a 3v3, manual would be turn based and the other 2 would be on auto.
However, in my suggestion the 3v3 would be 3 "individual" battles initially with each mon fighting an individual mon. That is the bread and butter of the system.
But, you could order the 2 auto mons to go after the same Mon so that it becomes a 2v1, that mon could call for help making a 2v2, 2 wild mons could gang up on an isolated auto mon and so forth. For manual, I don't know if having more than one Mon would work because it could defeat the purpose of the system so it's a maybe ?
The "basic" strategy of the system is divide and conquer, send your auto mons to weaken the surrounding mons, they can isolate them, gang up on them... A command system would need to be implemented to make orders more strategic besides just selecting an attack.
While the auto mons are doing there thing, your manual mon quickly defeats it's target, then you can either keep that mon on manual or go find an auto mon and make it your manual so it finishes its fight quicker