Current is passed through the wire which creates an electromagnet. This magnet spins and the wires in the stator cut the flux lines creating electrical current.
You're starting to sound like Snowbum himself! Yep, the initial exciting current for the rotor is provided by the battery. No gen lamp with the ignition on and the bike not running means no excitement.
A different type of generator can have a permanent magnet rotor and will start generating without introducing a current. Even an electromagnetic alternator may have enough residual magnetism to actually start the current flow, but not likely.
Yes, that magnetism might be enough to produce some juice at higher rpm's, but, as nhmaf pointed out, it is not reliable. Think of magnetizing a screwdriver with a permanent magnet, then dropping it on a hard surface to remove the magnetism.
You can have an
alternator, not just a generator, with a permanent magnet rotor. The VN750 I used to ride had such a setup, as do many older Hondas. They tend not to last as long as a wound rotor, especially with the modern resin coatings used charging system windings.
There should be no need for magnetizing a wound rotor. The whole point of them is that they do not rely on permanent magnets. A better, less time consuming, $40 solution to the low rpm drain on boxer charging systems is to install a high output voltage regulator. It will not increase the overall charging capacity, but it will make the charging system plateau at peak output lower on the rpm band