The problem with this is that the Arctic ice cap is floating on water. As any fule kno, a floating object displaces an equivalent weight of water. The sea level will not change as the ice melts.
You can easily prove this to yourself. Take one litre of water. It weighs 1kg. Now freeze it. It still weighs 1kg.; but now, due to a peculiar property of the H2O molecule, it occupies more than 1L. of space. Place this in a bucket containing several litres of water. The ice will float, displacing -- according to Archimedes' Principle -- 1kg. of water. Since 1kg. of water occupies 1L. of space, then the level in the bucket will have risen by 1L.
After 100g. of ice has melted, increasing the quantity of water in the bucket by 100mL., the remaining 900g. of ice will be displacing only 900g. of water. So the level will still be 1L. higher than it was originally: 100mL. from the meltwater plus 900mL. Archimedean displacement due to the remaining ice.
After a further 400g. of ice has melted, increasing the original quantity of water in the bucket by 0.5L., the remaining 500g. of ice will be displacing 0.5L. of water. So the level will *still* be 1L. higher than it was before the block of ice was introduced.
And by the time all the ice has melted, the quantity of water in the bucket will have increased by 1L. compared to what it originally was; but now, there will be no ice displacing any water.