Yes the alternator can do this,BUT so can the old relay and old or corroded light bulbs. Mine did this (and still does on occasion). Has been doing this for years and when I did end up rebuilding the alt it really didn't make much differance.

1990 Black Monty LS Over 300K' 1993 Isuzu Rodeo LS 4x4 46k (yes only 46K!)1989 Honda Transalp 600 Africa twin,