Aaron, no, there is no CDI.
The alternator provides current for three functions, with three separate coil windings (see shopmanual image):
1. Ignition (blk/wh wire) leading to the ignition condenser & coil under the seat.
2. Lights (yellow wire) leading to the light switch on the left handlebar.
3. Battery charging (white wire) via the rectifier diode under the seat.
There is no continuity to ground through the yellow and white wires within the alternator, and the ohmmeter reads infinite resistance for both wires.
There is continuity to ground through the ignition circuit within the alternator, but it could be that the points are closed but the coil winding is open too.
I think it's time to remove and examine it, and probably replace it.