As Bubbie found out, your electrical system is BATTERY operated by design...the charging system is made to SUPPLEMENT that power delivery. Once up to speed, the alternator is essentially "coasting" as most of the excess energy is "shunted" by the regulator and battery if in good shape is float charging.
When just starting, the alternator is essentially off and the battery is powering everything, Fuel Pump, EFI, ECM, Headlamp, Instrument, cornering lights etc. and then BAM you hit it with the 250A starter/solenoid draw for x seconds...which immediately takes away the surface charge of the battery (reserve) and the stored CCA within is the only thing sustaining the works.
As you guessed, if the battery has internal shorts, weak or damaged cells, it really will stress out your charging system, so once your stator overheats trying to keep everything running including making up for the battery losses it will fry...plain and simple. Having lowers on an Ultra will have no bearing on local overheating of stator windings.