from my understanding, most fertilizers are formulated to balance the typical minerals and alkalinity of tap water, so using a fertilizer made for tap water with rain water might not provide all the minerals your plant needs. they do make fertilizers (such as the MSU fertilizer) for sterile water sources, ie. r/o and rain water, but i'm not exactly sure if you really need to switch, especially if it's just a treat and not the typical way you water. hopefully someone more experience can give you better guidance.
but if you simply want to know if adding fertilizer to rain water will kill your plants, then no it won't
