Is the Antarctic only staying relatively cool because of the ozone hole?

LRG, the ice shelves that are melting play a major role in the global conveyor. Water is drawn under them and cooled about 1/2 degree. The temperature difference causes them to flow out as cold currents. They aren't isolated at all. One of these I know ends up in the Indian ocean and supposedly prevents runaway heating there. Anyway, when the ice shelves are gone, those currents will be gone too. I don't think anyone can predict the net effect on the conveyor. As a wild guess I think it might direct more warm water to the Arctic, but I couldn't prove it.