this is indeed true.
7/8ths or so. this is because ice is only slightly less dense than water. (water's at its most dense at around 4 degrees C, I believe...)

edit: and because the floating ice becomes more dense when it melts, it has less volume, so the water level drops *slightly*. would be counteracted by the huge amount of ice sitting on land melting though
(Fantastic Mr Porter is bored, and wishes it was, Sat 13 Jan 2007, 1:34, archived)