Is it was technically possible for a superhero that senses radio waves (like low frequency EM) to “hear” the radio?

This superhero senses radio waves a bit like we can see visible light, though not with his eyes. He has a 360 degree field of radio vision, even wider than hearing as he senses these waves directly with his brain (this part doesn’t need to be scientifically accurate, handwaving it to magic is fine with me).

I’m not entirely clear on how radio works. I know there is a carrier wave and all that but even when looking through Wikipedia I am not clear on if there’d be any kind of transformation needed to the signal. I have been told by music professors that when they used to play guitar on rainy days their amps could pick up some radio stations but then again amps transform the electric signal from the guitar into sound. The brain and auditory neurons don’t necessarily work that way… do they?

Possibly.

Keep in mind people have heard demodulated radio signals from their tooth fillings, and early radios were passive and extremely simple.

For simple radio signal modulations namely AM (including SSB and spark-gap) the brain would only need a rectifying junction and a resonator both of which could be natural features of an organic mass like the brain that at some point was exposed to crystallizing heavy metals by accident or by design. It wouldn't be tunable per se, but the brain wouldn't necessarily be limited to just one junction/resonator pair which could be microscopically small on the scale of neurons so there could be enough present to cover a wide range of the spectrum at once. It would be very noisy and would depend on the brain's ability to discriminate signals such as when focusing on a particular person's voice across a table in a large crowded room.

Unfortunately it's hard to think of applications of AM anymore that would be of interest to a superhero. Evil geniuses would likely use more exotic forms of modulation including encryption which even a superhero brain would likely struggle with.

Probably no

Out of the box, I can think of two reasons that a superhero with a 'mutant' power to detect radio waves would not be able to hear music over the radio.

The first is that our senses require parts of the brain tuned by hundreds of millions of years of evolution to interpret physical phenomena into sensory inputs. Not only do waves of light hitting our rods and cones have to be translated into electrical signals in our visual cortex, but those electrical signals have to translated into abstract concepts like "red" and "far". A mutant ability to turn radio waves into some neural signal is one step, but being able to interpret that neural signal is another thing altogether.

The second reason is exactly the carrier waves that you mention. The sound signal of a radio is embedded into a carrier signal, through either amplitude (AM) or frequency (FM) modulation. You can't 'listen' to a radio wave, because the frequency is too high, but if you could 'hear' a radio wave like sound, then AM radio would just sound like a signal that is getting louder and quieter over very short periods of time (milliseconds), while FM radio would sound like a signal that was getting higher and lower pitched, slightly, over very short periods of time. A radio relies on a band-pass filter to remove the carrier signal and get the interesting stuff, in the frequency range of the human ear.

But, ultimately, a brain that detects radio waves is basically impossible, you can do as you please. These are two good reasons not to have the superhero 'understand' transmitted radio waves, but since the whole situation is fantasy, you can pretty much do whatever you want.