I wouldnt expect it either.
However, one thing i didnt like about SH3, when a crewmember is dead, he is just red.
With all parts of the sub accessible it would be a real disappointment if you searched the whole boat and this crew member was just "gone" and no longer anywhere to be seen.
I would say that in a bunk, with a sheet pulled over his head would work.
There he would remain until you surface, order all stop, and physically click the body.
at this time a short burial at sea sequence would take place.
Perhaps render 5 or 6 crew on deck sliding his body overboard before heading back below or someting... nothing fancy.
AT A MINIMUM: you should be able to right click the body on the crew management screen and select "Burial at sea" option. and then the crewman simply disappears.
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