Im pretty sure the answer to this is NO it will not over flow because ice takes up space in the glass which is called diplacement so as the ice melts (returns to its liquid form) it just takes the place of the ice (its solid form) since ice is just water in a solid form as it returns to a liquid form its just replacincing the space it took up as a solid rather it fills in the now empty space that it took up as a solid , or something like that. RIGHT