I don't think the dash lamp will light if there is no circuit to the alternator rotor winding, as will be the case if the brushes are worn out.
That means it won't indicate lack of output, either.
However, if you have some bad diodes, you have the correct voltage, but no current, so you run the battery down starting and using the headlights, no dash indicator until the last diode gets weak. This happened on the 220D -- I would have to jump it once in a while, and then recharge the battery. Ate alternator belts, too.
I took the alternator out (after I got a used on at the u-pull-it that was also bad), figured the bearings were bad since it was noisy.
Took it to the rebuild shop and got essentially a new alternator in return for $110. New rotor, new stator, new diodes, the guts were knocking together! Bearings were fine. Note that these were actually used parts -- new was more like $200.
1972 220D ?? miles
1988 300E 200,012
1987 300D Turbo killed 9/25/07, 275,000 miles
1985 Volvo 740 GLE Turobodiesel 218,000
1972 280 SE 4.5 165, 000 - It runs!