The electrons in a wire generate a magnetic field, that's right, and in a coil, much moreso, because the fields from the parallel wires reinforce one another. A DC current will generate a steady state field, and an AC current will generate a varying field. This is why I've been talking about AC and DC voltages and currents. The AC component (where the audio info is) is not affected in any way by the DC component, be it electrical current or magnetic field.
If you have, for example, an output transformer of an amplifier driving a speaker, you can drive a DC current through the primary along with the signal and it will not appear on the secondary, even though the DC component is making a non-varying electromagnet of the primary. This is because inductance (which is a magnetic effect) works on AC current but not DC. When you apply Ohm's law to inductors, there's a "dI/dt" term, which is the change in current with respect to time, and if dI/dt = 0 (meaning the current is not changing over time, i.e., it's DC), the inductance term totally falls out of the equation.
The reason a magnet deflects an electron beam in a CRT tube is because the electrons have been accelerated to a high velocity. Electrons in motion generate a magnetic field, and that's a good example of that, but it's an example of two "DC" magnetic fields interacting. If electrons could be moved by magnetism alone, you wouldn't need a battery in your car; all you'd need would be a big permanent magnet.
Did I mention that I have a degree in electrical engineering? Sorry if I get long winded, but that's what engineers do, or so my wife will tell you... ;^)