Sea ice is floating ice. If it were to melt, it would make not one bit if difference in water levels anywhere.....
I've yet to see a full glass of ice water overflow once the ice melted.....
As to your example of the glass of ice water - that's not quite so. You have assumed that the water displaced by the ice would remain at or close to zero Celsius. Water at 8 Celsius has roughly the same density as water at zero Celsius. Because H2O is densest at 3.98 Celsius, if global ocean temperatures were to rise pro rata sufficient to melt all the polar sea ice the volume occupied by the present mass of the oceans would increase.( Ignoring evaporation which in practice one would not be able to do)
Also the sea ice melting would reduce the overall albedo of the polar ice caps further increasing the overall tempreatures of the oceans.