If you fill it with ice that is twice the height of the glass, then yes it would. All the ice in the world is not even with "the top of the glass."
The “stacked” ice you speak of is mostly located on the interior of the continent. The temps on the continent are nowhere close to allow ice to melt.
The ice that is melting is on the ice shelves. This ice is located along the coast. Some areas along the coast do get warm enough for some of the ice on the shelves to melt. This is ice that is already in the water.
Climate change alarmists pray on the ignorance of physics.