As you suggested, some bikes have separate coils for lighting and ignition (like the Gilera bike in the other thread on 6v AC volt regulator). It looks like this bike ('69 Wards/Benelli) has a single generator that is the sole electric provider. This makes sense, because it's got coil+battery ignition, so the generator merely has to keep the battery charged for everything to work.
A bike with magneto + coil ignition is more likely to have separate coils for lighting and igntion, since spark and lights have different needs. The quick kick is the only source of the ignition spark, and that coil has to be made for that.
As for losing the emergency push start if I convert to 12v, I surmised that. In short, if the batterys dead the instructions say that that upon flicking the "emergency battery bypass switch," you can push-start the bike. It's hard to parse out the wire diagram, but I think this disconnects the battery from the generator, so that the all of the generator's current goes to the ignition coil.
So then the generator acts as a starting magneto. But the generator isnt a very good magneto; kicking the starter lever isn't enough. You have to give the bike a vigorous push start. Given that the generator barely functions as a starting magneto, I'm guessing that changing to a 12v ignition coil wouldn't allow it work in the emergency fashion.
Attached are three different wire diagrams. Two are factory, and one was made by Alec_t on this board (thank you, Alec!). I've also attached a link to the owners+workshop manual.
https://www.dropbox.com/s/e94r7zxj4x41dbf/250_350_Service_Owners_Parts.pdf?dl=0#