If one of the destroyers is able to detect your presence with her sensors (even periodically) they will never let you go, why would they?
Nearby destroyers can also "communicate" with each other, don't forget that...And be very careful regarding your sound signature. Even the early escorts can hear quite well.
Try to convince them that you are already "dead" or that you somehow managed to leave the area...
Early escorts in TWoS are nothing special really but they are also not stupid...