A failed or failing regulator will cook a battery, I’ve had a mechanic warn me about that when I was.... 17 or 18. I didn’t have a lot of cash so I got the regulator repaired only. Not long after, I replaced the battery, it was dead one morning when I was heading to work. Several vehicles later, I had another v/r go, replaced regulator, but had a pretty new battery, so I chanced it and did not have any issues.
When the Duck regulator went, it cooked 2 batteries, my old one, which lived on a battery tender but was about 4 years old and my fancy new Shorai lithium iron. Once I knew the regulator was dying or dead for a fact I was nervous about being invisible (on the bike, lights are always on but when the regulator dies, the circuits go out, so no headlights, brake lights or signals).
@FordTechOne confirms the electronics will scram before permanent harm, but, I still maintain you don’t want them scramming while you’re driving, so I’d be ok driving it on to the flat bed but I wouldn’t take it further than around a city block.