Why have regulator in the mouth while climbing the boat? If you fall back to the water, you will pop to the surface in few seconds - you just got back from the water, you were positive. If your BCD fails at the same time - you are still positive if properly weighted. Moreover you will have plenty of time to recover your regulator. If you can't find your regulator, you will have another reg (necklase, air 2, octopus - whatever the configuration). If you fall, hit your head, and pass out - the regulator will fall out of the mouth anyway.
In contrary, climbing the the boat with all the gear is a physical exercise and I'd prefer to breathe fresh air instead of trying to suck remaining air from the tank. I just keep my regulator either clipped (if it's a long hose) or just hanging infront of me (if short). If I fall, I'll grab it right away and I can breathe from the clipped regulator without unclipping it (in case of emergency).