If sea levels rise, there would also be more area under water. This would produce more evaporation.
If temperatures rise, this would produce more evaporation.
Even if we suppose a huge chunk or the entire glacier plops into the ocean, it would seem that most, if not all, of this additional water would end up back in the atmosphere and/or back into glaciers. I don’t know enough to speculate on a time frame.
You are correct on all those statements.