I agree, there isn't much 'groundplane' with that power supply. But that depends on the frequencies you listen to with the antenna. A "perfect" groundplane would have a radius of 1/4 wave length at the frequency of use. Larger certainly doesn't hurt, smaller makes for 'less' of an antenna.
That magnet/magnetism has no electrical significance. It does have a mechanical one, it holds the thing on metal. The electrical significance is that the magnet makes up one 'plate' of a capacitor, the metal it's stuck to makes up the other 'plate' of the capacitor. There's a capacitively coupled connection to that metal and that's the 'groundplane' (actually, the 'other half' of the antenna). So the size of the metal that antenna is stuck to makes a difference. It doesn't have to be a solid plate of metal though, as long as portions of it are the right size. As in add one or more wires to make the length from the center of the magnet something close to a 1/4 wave length, for instance.
- 'Doc