There is a difference between a dead battery and a defective battery. At least, there can be. A dead battery might just be low on charge and an alternator should be able to charge it back up with no damage, but a defective battery with internal shorts that forces the alternator to operate at high load constantly certainly could cause it to fail. The flip side is that a defective alternator can fry a battery, also. So replacing a battery and having the new one go bad soon afterward might mean the alternator was bad to begin with. A depressingly large number of people don’t test the charging system after replacing a battery.
There are also differences in alternators. Some can source larger currents than others and would be less likely to be harmed by charging a dead battery. Also, alternators generally are providing current to all electrical loads when the engine is running, the battery only provides power when the engine is either not running or idling too low for the alternator to keep up.
So, there are a lot of “ifs”, “ands”, and “maybes” to the answer.