I think the early W124 models had underpowered alternators anyway, and as they get weak, the accessories are the first to get starved of juice.
I believe that the voltage regulator is built internally in the alternator anyway.
You are probably getting a nominal charge to the battery, but it's only going to get worse. When it does, the engine management systems get affected, and your car will act like it's in limp mode.
Have your charging system checked to make sure, but I'm not sure it's detected at an early stage. I had an alternator once that checked out fine, only to have it fail a week later...
2009 ML350 (84K) - Family vehicle
2001 CLK430 Cabriolet (71K) - Wife's car
2005 BMW 645CI (124K) - My daily driver
2012 Mustang V6 (60K) - Daughter's car