No, it won't. Floating ice displaces an amount of water equal to it's own mass, so if all sea ice melted the water level would stay the same, not decrease.
Actually, it may be a bit more complicated than that, since ice would melt into fresh water which is a bit less dense than the sea water the ice is displacing. So, melting sea ice would slightly reduce the density (and salinity) of the ocean and perhaps actually raise sea level a little bit. Changes in the overall ocean temperature would also affect sea level, as water density changes with temperature. Regardless, melting sea ice would not really cause sea levels to drop in any significant way.