Nice thinking, crazy legs, but flawed.
As CrazyWolfman points out, the fact that floating ice displaces its own weight of water, ,means that when it melts it won't make a difference to the water level.
(Try this yourself my marking the level in a container of water, firstly with ice cubes floating in it, and then after the ice has melted.)
Unfortunately, the two largest ice sheets on the planet are the Greenland and Antarctic ice sheets.
These are quite happily sitting on dry (albeit frozen) land, and are not floating about in the oceans, therefore, they do not displace any water - so if they melt, there is only one place that water will end up.
Try this also with your container of water, and a separate tray (with some very large chunks of ice frozen to it) carefully sloped at an angle towards your container.
Mark the level of water in the container.
Now wait for the ice to melt a bit so that the drips of water end up in your container, or, alternatively, wait 'til the whole frozen chunk becomes detached from the tray and slips down into container with a large splash.
Hmmmmm..., do you think the water level will go up then?