In my experience with cb550, everything quits when you disconnect the battery at idle. I'm pretty sure (but I cannot swear) I've disconnected the battery at higher RPM and it kept running until the revs dropped down, then it just died. I'm unable to reproduce that experiment at the moment, but I'm sure you are capable of doing this yourself.
Also, there's no way in hell the bike will start with even a low battery, let alone no battery. Not by kicking, not by bump-starting, nothing. Mind you, I had already converted to electronic ignition, which I understand does not work at all when voltage is low. When I had points, it was much easier to bump-start when battery was low.
Yes, I could see a capacitor-driven system storing energy for periods where the alternator could not produce any. However, why not just use a battery at that point? Battery would serve as a capacitor.