It’s heat that typically kills–an alternator can probably handle more of a continuous load this time of year, at least in the colder climates.
Everyone should have a battery charger anyway. You can get cheap ones at, ahem, Walmart.
I have been using a 6 amp charger to charge weak dead or rundown batteries for more than 50 years, Yes the same 6 amp charger for all 50 years. Never had a problem with it or the battery or alternator. Use it on the lawn tractor also.
I have had a couple of alternators go but they went while driving and not in conjunction with a discharged battery. I loved the old days when you could replace the brushes in a Chrysler alternator for 25 cents with a Phillips screwdriver on the car in a minute.
The 69 Dart mentioned above had an alternator, Chrysler products went to alternators in 1960.
@kenberthiaume, keeping it as short as possible here’s an example of an alternator done in because of an outside issue. It’s motorcycle related but the principles are the same.
Harley quit charging - volt. regulator tests bad. Replaced with aftermarket reg a common practice. - fine afterwards.
Some point weeks on system quit again. Tests showed regulating winding in alt. bad.
Replaced alt.- things fine for a while.
Repeat above. Regulating winding out again. Replaced alt. 2nd time.
Time passes - goes out again. Regulating winding again. Replaced alt for 3rd time.
Dropped all 3 stators into the carburetor solvent for a week to dissolve the insulation and unwound all of them. The regulating winding underneath the main windings were fried on all 3 stators. So; this makes the reg suspect as battery and cables are good.
The reg (solid state enclosed in resin) has a 4 pin molded plug with a heavily sheathed loom. I used a razor blade to cut the loom open and what did I find? Not 4 wires, but 3. The reg was manufactured WITHOUT the regulating lead which controls the alt. output. The tiny hole in the molded plug was a dead hole.
This allowed the alt. to run away with itself; usually during higher speeds on highway trips.
So what was happening is that the alt. was looking at this as a vehicle with no battery or a stone dead battery and frying itself accordingly. Granted this example is extreme but kind of makes the point about what can happen when an alt sees nothing at the end of the charging trail… 
Harleys have automotive-style alts? I guess you learn something every day. I’ve only dealt with PMAs on two wheels…but none of those were H-Ds.
They don’t look like automotive alternators and are permanent magnet but work on the same principles. They’re not that easy to change as they’re buried in the primary chain case which means the clutch assembly and all has to come apart to get to them.
HD went to alternators in 1970 on their Big Twin models. Prior to that they used a 12 volt, gear-driven generator. Backing up even more, that was preceded by a 6 volt 2-brush generator and a 6 volt 3-brush before that.