Not in every case. Some 1-phase KZ650's can cope with the Dyna S, but whenever a charging issue comes up on a 78-79 KZ650, often the Dyna S is involved.
One thing to note is that ignitions use slightly less electrical power at higher RPMs (I realize it's counter-intuitive), so even if your charging system is totally dead, the voltage will actually climb a few tenths when the engine is revved. This often tricks people into thinking the charging system is working a little bit.
If you rev it, and it only gets a little above 12v, then there is definitely something wrong. You can go through the tests procedures in the manual to try to narrow down whether it's the stator or the reg/rec. Since your battery only gets to 12v, you may have more than just a weak stator problem.
But if you are running the Dyna S, (your post didn't actually say whether you are using one, or are thinking of using one), you may want to consider a 3-phase conversion. You have to get a 3-phase stator, and 3-phase reg/rec, then add one extra yellow wire from stator to reg/rec. Depending on the reg/rec, you may have to add a brown wire from the harness to the reg/rec as well.
Yes, the reg/rec needs to get some air to it or it will overheat. If you are using the frame as your only ground, that often causes some hard-to-troubleshoot problems. It's far better to run dedicated ground wires to everything, and also connect to frame AND motor for grounds.
