Sorry, but while it adds fresh water *ICE* to the ocean, it gets added almost entirely as ice without undergoing a melt phase until it gets far north of Antarctica. So you aren't getting a lot of fresh water added to the Antarctic ocean. You're getting ice (which is, indeed, fresh water) added to the ocean. It gets a considerable distance from Antactica before it typically melts. (Except, of course, a little bit, which lubricates the flow of the glaciers.)
OTOH, if the sea ice were trapped around Antarctica, I suppose it would melt. Fresh water has a higher freezing point than salt water. But I don't believe that's what typically happens.