The radio guy also operates the radar after it becomes available.
According to the manual, if you hit the "R" key your butt will be plopped down in front of the radar apparatus, and from there it would appear that you can indeed become the ship's radar operator.
Apparently the same goes for the sonar station. Just hit the "H" key and listen to the song of the seas (or the roar of the desron as it dumps ashcans on your head).
You'll want to familiarize yourself with the game manual for more professional instruction.
And after reading that... I'm off to test it out for myself.