Except the whole point of the fleet is to stop that from happening. In this case resupply would be easy and they would not suffer as badly in the winter. There will be no food and people will begin starving.
I know that in time the city would starve... But they wouldnt ran out of water since they had an excellent water system... As for food i believe that Constantinople could hold till winter before running out of supplies and the harsh winter of this area would have forced the Arabs to retreat at least temporary thus allowing Constantinople to resuplly from adjacent cities (if not by sea) and then wait for the Arabs to return (if they return).