Fortunately. MBZ alternators have lots of cooling and seldom overheat or fail. It is part of the DIN testing required to get certified in Germany. All the 'accessories' have to be able to run at full load at any speed--from slowest idle to maximum RPM/road speed indefinitely in any climate condition for which the car is certified.

However, a 'dead' batery does place an extraordinary load on the alternator as it tries to recharge the dead beast. Batteries fail from slow aging (lead oxide and lead sulphate flake off the plates, fall to the bottom, eventually leaving no active surface or shorting out at the bottom.)

Low voltage will cause a host of weird symptoms.