Yes, Eagle has a ULP for making small etched spots to help center the drill : drill-aid.ulp
As for the original question, I can understand the need to have a clear zone around a hole, but for hand drilling, I would still keep a pad there with an etched center for locating and centering my drill.
Sorry, can't answer how to do it in Altium. In Eagle, use a round polygon as if making a copper pour. You can also use a keepout layer and a regular geometric shape, but that would make it harder to put a small pad in the center.
John