michinyon:
That is, if I mechanically spin an excited induction generator/motor, I should be able to form 3-phase power out.
No, you won't.
He most certainly would be able to, if he follows standard procedures for either a grid connection, or chooses the correct capacitor values for the stand alone connection, as described (for example) in the Wikipedia entry: Induction generator - Wikipedia
In induction generators, the reactive power required to establish the air gap magnetic flux is provided by capacitor bank connected to the machine in case of stand alone system and in case of grid connection it draws reactive power from the grid to maintain its air gap flux. For a grid connected system, frequency and voltage at the machine will be dictated by the electric grid, since it is very small compared to the whole system. For stand-alone systems, frequency and voltage are complex function of machine parameters, capacitance used for excitation, and load value and type.
You can make generators out of single phase induction motors too. Here is an experimenter's account: Induction Generator