Elaine, I would never water my plants with ice cubes. I have over 400 plants! That being said, I cannot tell your how many people I have talked with or sold plants to that said that is exactly the way they water. Some have done that for decades and their plants seem to do fine. Scientifically or anecdotally, I don't know whether this practice hinders blooming. My concern is not the water than slows waters the plant as the ice cube melts, but the fact that the ice touches any part of the plant. That's what's hard to get around.
P. S. I have never watered via ice cubes, even when I only had a handful of plants, and really see no need to ever do so.