If it’s a small amount, I don’t think it will matter much.

If it’s a huge amount, it will become part of the water cycle systems. Oceans/seas/lakes evaporate surface water, which become clouds, which move around, then hit mountains and other things, get squeezed, release rain, which generally flows back to oceans via rivers. It may get stuck in lakes, or as snow on mountains, but in the big picture that is temporary.

Adding more water will likely put more in the oceans, as that is what holds most water right now.

Based on what I read about melting icebergs, If you add enough sweet water to oceans, it might mess with how water flows between oceans, which upsets how air flows across the planet, and thus it messes with large scale weather patterns. For example, Europe benefits massively from patterns that feed it warmer air.

Imagine Europe getting the same low amount of rain as the Sahara, or the Sahara suddenly getting the rain Europe gets right now. It’ll be a catastrophe if that persists for decades or longer.