I ran "Bait and Switch" with a friend last night to see how it handled with multiple players. It went pretty well but there's a part where you do something technobabbly to jam the enemy's transmissions. This creates an FX - Static Interference 01 asset that disappears when the fight ends.
My friend was flying an Obelisk, and his hangar pets (Advanced Obelisk Swarmers) completely froze due to the interference asset. They would launch and then park themselves in space (naturally, with no shields thanks to the interference). After it disappeared, they stayed parked, but he got them back after we went to the next map.