Ultimately, you are not wrong in asserting that a US Fleet Type boat could both transmit and receive at radar depth. The only provisos are that they would have to have a VHF rig, and the communication would be limited to the capabilities of that gear. In other words, Fleet units close enough to receive the signal could do so, but by no means would it be possible for the boat to contact a ground station on this gear unless in range, not blocked by any interference, and the ground station would also need to have the appropriate gear. Additionally, I make this observation: I have been at radar depth on approach to a target in high sea states, had the periscope raised just enough to clear the housing, and had it be regularly washed by the wave action. So there also would be that factor of limitiation on the VHF.
[EDIT] Found this on Wiki regarding standard range of VHF transmissions:
http://en.wikipedia.org/wiki/Very_high_frequency