Starter stuff could be ammonia used to cycle a tank, or beneficial filter bacteria to help get the cycling process done faster.I haven't read the label but assume that the API starter stuff is a bacteria base. I mean what else would tank starter stuff be?
Stagnant water generally contains no or low levels of oxygen. If there is rotting matter in the stagnant water, then that will produce ammonia. But in a clean filter the water will simply be low in oxygen and that won't have any effect on the undergravel filter.