Not really. If the inductors are VERY close together, like wrapped around the same metal core, you will have a transformer, which will transfer the signal from the primary (input inductor) to the secondary (output inductor). This is what audio transformers do. The signal is transferred by magnetic coupling, not electro-magnetic waves (as in RF). Magnetic coupling works better at low frequencies (like audio).
The antenna (inductor in your description) needs to be tuned to the frequency you are sending. It is theoretically possible to create an antenna tuned to 1KHz or so (audio band) but it will be BIG and will require lots of power to transmit.
Audio is transmitted over radio waves by attaching it to a higher frequency. The simplest method is Amplitude Modulation (AM). Frequency Modulation (FM) has also been used for a long time. Higher frequencies can transmit using a smaller antenna.