Can an experienced airplane spotter identify planes only by sound?
Yes it is possible, although it is kind of hard to prove it over the internet.

Generally the type of engine (propeller / turbo-fan / turbo-prop etc.) is quite easy to distinguish as they make very different sound. I can also tell a Rolls Royce engine from others because Rolls Royce engines make a quite "harmonic" and "warm" sound as it powers up.

Now here is the fun part: I correlate the sound with the type of the plane by comparing the Doppler effect as the plane passes by. It tells you how fast the angular velocity is in relation between you and the plane. The variation in loudness gives you the approximate distance to the plane - if the plane is far away, its loudness would change slowly. Combine that with the geographic location of yourself and the flight paths of planes, it gives you the speed of the plane.

The speed of the plane is important because it tells you the size of the plane. If I hear a loud multi-prop engine moving slowly, I'd bet a transport plane, something like a C130. If it is moving quickly, I'd bet an aerobatic aircraft.

The location where I live is directly under one of the SIDs of a major airport. Planes are usually ~3,000 feet when they pass above me. One thing I notice is that long route planes like Boeing 777 or Airbus A340 makes a noticeably louder noise. This is because these planes carry a lot of fuel on takeoff, and their climb performance is restrained compared to short haul airplanes, meaning they pass above me at a lower altitude, hence the louder noise. I cannot distinguish from sound if it is a B777, B747, A330 or A340, but I know it is not a B737 or A320 unless the pilots fly slow and low.

I confess I have an unusually good hearing ability. I often hear faint sound or noises which others cannot notice. I am also a musician.