There is a transition period between low current output and high current output on an alt. Your eye is very sensitive to light and it takes less that 1/20th of a second flicker for you to notice the dimming. The voltage regulator must note a drop in voltage and correct it, this doesn't happen instantly and thus the dimming. This is one of the rare ocassions where a cap will actually do something productive. A cap can ease the transition and minimize the appearance of the dimming. It will be a very slight dimming ,barely perceptible, and then by then the alt will have kicked in. Note: there will not be an audible difference, but it will reduce the noticable effects of dimming lights.
As far as the whole belt thing goes, without changing the size of the pully on the alt, you haven't done anything by just going with a smaller belt. You have to adjust the ratio between the driving and driven pulleys to have any effect. You have to change the size of one or the other.