The Sulaco is automated, yes.
Even if they left another squad on the ship, it doesn't necessarily stop the story happening:
Marines escape the hive and are able to alert the b team about what happened, and that their drop ship is en route for immediate evacuation. They'll be back on the Sulaco after picking up Bishop.
Drop ship crashes as per film, rendering marines unable to communicate with Sulaco.
Since the marines have just confirmed there's a dangerous parasitic organism on the planet, and then promptly went silent, they don't even know if the b team will try to extract them or assume they're lost.
After several hours the marines start to think they're not getting extracted. With the processor ready to blow, Bishop goes to the colony transmitter.
Bishop connects with the Sulaco. Because of the biohazard of the Aliens, the b team won't attempt extraction. They've been waiting to see if they could resume communications.
On account of the whole quarantine risk, Bishop requests to remote pilot a drop ship. The survivors will be quarantined in the hangar bay.
Movie happens as usual, since the hangar will be empty Ripley still has to yeet the Queen herself.
Really the only movie that hinges on there being no b team is Alien 3.