What's more important, the singer or the microphone?
Obviously, the singer.
But the wrong choice in a microphone can affect how the singer's sound is perceived. In other words, it can give a good singer tone that a given listener may not like. That's a subjective decision, and changing the mic may or may not make you like the way the singer sounds.
A magnetic pickup is a microphone, though its method of transduction is different from other mics. This is why pickups feed back, just like conventional mics that rely on diaphragms do. I would imagine that I don't have to take the comparison much further...