The camera hardware implements the readout upon command from the application processor (what you'd normally call the "CPU" of a phone), and the readout does have to be carefully timed in order to ensure a consistent exposure across the frame. So, whether the phone is overloaded or not will not affect readout speed (and therefore the rolling shutter effect).
This does not preclude the possibility that some other photographic process was stalled, such as HDR stacking.
This does not preclude the possibility that some other photographic process was stalled, such as HDR stacking.