half dead battery
 

will slow cranking with a near death battery cause any harm to the starter motor :icon5:

The lower voltage will raise the current draw thru the starter. More heat, so maybe. Why delay getting a new battery until you destroy something or until the car quits?

Yeah, heat is bad. And, this starter takes so little current, that running it low is really a low battery. Why is it low? Alternator going bad? Try putting it on a charger at night, still in car, if you can to limp along. Also, bad battery will weaken or kill the alternator. Then you need a battery, an alternator and a starter all at one time. That sucks. Been there, done that.