AIS is required for large ships in many if not most jurisdictions, to have it turned off is suspicious in itself. If you turn it off then re-appear later on somewhere else having had to traverse the area where the cables where at the time they got damaged, that's suspicious. You could turn it off in port, head out, cut the cables then return and turn it on again, but the window of time you had it off would straddle the cable damage time, and there's a high chance you would have been documented (video, radio traffic) leaving port in that time, and depending on the departure port it may be hard to leave without AIS on as the authorities may notice.

fishing boats and military often have it off btw.