Are they though, in the straight ? I'm not sure it's such a great move, TBH:

Given that the baddies clearly can locate ships and see that there's no transponder, and come to the conclusion they need. "Hmm, it turned off transponders and is now moving toward the straight. It's a tanker, and not one of ours, or Russia's or China's. Let's bomb it!"

Also, pragmatically, you could look at the transponders suddenly not showing up anymore as a sign of attempt of passage, especially if they show up later on the other side.

But yes, that would no longer be very realtime.