Would the melting of the ice flood the world?

Unfortunately, that only holds true for sea based ice. If there is ice in the sea then it already displaces seawater equivalent to the amount of water held inside it, nobody disputes that. The problem is caused by the melting of land based ice sheets which do not displace seawater to start with. Add to your analogy a surface which is tilted towards the glass and put some ice on there, watch the water level as that ice melts.

The reason the melting of floating ice won't itself have an effect on sea level is because the ice displaces water when it's floating and after it had melted, it's part of the sea instead of displacing water as a solid object.

It's ice sitting on land that would raise sea levels by melting because it's not displacing sea water.

Once the sea ice melts, it'd be open water, which is much less reflective than ice, so it'd absorb more energy from the sun. That should offset any cooling of the water caused by the ice melting, although the ice itself will remain at an constant temperature while it's melting due to the energy taken from the sea and sunlight going into breaking up the ice's structure instead of increasing temperature.

I once did an experiment in chemistry class where I watched the temperature of melting ice and that of boiling water. They remained constant at 0C and 100C respectively because the energy the burner I was using was going into the breakup the ice crystals and move the water molecules further apart rather than increase the temperature of the melting ice or boiling water. Once the ice is all melted or the water is all boiled, the temperature can increase again.

The melting of ice floating on the ocean wouldn't have a significant effect. The warming of water would cause expansion. The melting of ice on land has an effect.\

http://en.wikipedia.org/wiki/File:Post-Glacial_Sea...

Most of the rise in sea level has been due to melting of continental glaciers since the last glacial period.

Sea levels would not rise much. ice has more mass, so, of course, if it melts, there would be less mass. We would only have to worry about the 10% of the ice that floats above the level of the sea, which will not be significant enough to do much of anything.

if the ice caps, icebergs and glaciers of the Earth were to melt, raising global sea level, this would pose a serious threat to tens of millions of people living in cities along the coast of every continent.

The simple answer to your question is no.

Sea levels would rise, but there would be plenty of land remaining.