11.5V = Dead Cell?

My buddy has had an electrical problem with his '63 Dodge 440 (383 engine) for quite some time. He says the car "blows" voltage regulators when he turns the headlights ON. He has tried multiple mechanical & electronic voltage regulators (with a known good ground). The alternator has been bench tested "good". He has replaced the under hood wiring (harnesses from Evans wiring). He has added a volt gauge (spliced into the ignition "run" side of the ballast resistor) and with the engine running it reads 11.5 volts.

Will a dead, or dying, battery cell limit the voltage to the 11.5 volts?