re: "- - - heavy, rocky core- - - "
sure, but that is covered by the layer of metallic hydrogen, which grades up into a "sea" of liquid hydrogen which grades up into the "atmosphere" of gaseous hydrogen
There may be one or many interfaces in this sequence, and they're likely to be dynamic - like clouds on Earth. The density and radar reflectivity contrasts will be small EXCEPT for the metallic chydrogen, which should be an excellent conductor and reflector
Unfortunately, and EM radiation would be attenuated to essentially zero before it reached this deep
So, unless you're planning to send a science-fiction style super-heat-and-pressure-resistant bathysphere to Saturn to do radar sounding from deep within its atmosphere, the issue will remain a moot point.