QDM
If you have a 400MHz EPIRB with you, definitely, and everybody should have one. But at £600-£1000, very few people going cross-channel will though. I have one in my emergency bag and would hope to grab that on the way out. But if you only just managed to escape in your drysuit, the chances are that you didn't manage to retrieve it...
Timothy
Presumably if it was badly damaged then it would? Otherwise, how did the water get in?