Nothing, if the alternator is good the engine should keep running.On the other hand if the alternator is bad the engine will die/stall.
In a modern car with sophisticated controllers (ECM, BCM, TCM, etc.), NEVER DISCONNECT the battery with engine running. These controllers have semiconductor chips that are sensitive to voltage spikes and transients which become pronounced when battery is disconnected.. Even the power diodes in the alternator can be stressed and eventually damaged.