jcjant, Christiaan --
The ELT(s) would be of the mounted type, and sink along with the ship no matter how much buoyancy capability the small ELT box has. And many of these have NO buoyancy at all.
You're perhaps confusing ELTs with PLBs and EPIRBs, some of which do float and are meant to be carried out of the aircraft and into the liferaft with the evacuating crew. Liferafts may have their own locator beacons as well. But if nobody had a chance to evacuate, no ELTs or PLBs will have made it to a point when they could have started to float and transmit. The regular ELTs would have transmitted after being triggered, as long as their antennas remain above water.
Also, they are guaranteed to transmit their signals only as long as their batteries permit, the unit remains upright with the antenna out of the water, etc.