a bad alternator could definatly do that.
They produce less voltage at idle anyway, and as they start to go out, and make less and less voltage, it becomes a bigger problem at low rpms.
Consider yourself lucky. All my alternator just cetch fire.
lights dim, car cranks slowly, when you turn the vent on high with the lights on, the voltage drops way down... when you have the alternator tested at your friendly parts store, it test 'bad'.
I changed out the starter relay and fixed all kinds of voltage gremlins in my daughter's 91. $10..just a lucky guess! That was after new cables,battery and tested the alt!!