You are asking about this circuit
and want to know whether this is a radio transmitter/receiver system.
No, it's not.
First, everything is DC. There is no radio propagation at DC (0 frequency).
Second, although the question mentions antennas, there are none in this circuit. Radio transmission and reception requires antennas. These aren't always deliberate antennas, but there still have to be circuit elements that act as antennas.
At best, you get some transformer coupling between the two inductors, but that's not radio. The same is true for capacitive coupling. Of course both of those don't work at DC either.
As a side note, the reverse diode in series with the LED will prevent current flowing thru the LED at all. The LED blocks current trying to flow thru it in reverse, and D1 blocks current trying to flow thru the LED in the forwards direction.