However, I would definitely try to apply the recommended amount of fertilizer (for the correct stage of growth) now to get that grass established. A little fertilizer will probably wash into the pond, but right now the pond probably has low fertility, so it is the best time to have some fertilizer reach the pond.
Yep! If you wanted to save some $$, get a soil test done specifically for turfgrass. That will tell you exactly what fertilizer and lime is needed so you don't over fertilize. A $10-$12 soil test is a lot cheaper than buying too much fertilizer.
Especially important now that events in Russia & Ukraine have sent fertilizer prices skyward!