No, but if junk gets in water, it becomes undrinkable. Also, depends on the number of ice cubes doesn’t it? That is the key? Are we putting more “ice cubes” in than the glass can handle?
Not the point, and I’m not talking about putting junk in the water. Pollution is a separate issue.
Put some water in the glass, oh, maybe two-thirds of the way. There’s your ocean. Then fill up the rest of the glass, below the rim, with ice cubes, or ice wedges, or even chips. There’s your ice caps and icebergs, if you want some.
Let it all melt. The glass will not overflow.
It’s simple physics - Displacement 101.
PS - the number of ice cubes represents the existing ice caps. impossible for it to be “too much,” since they’re already there, and our shores are intact. There’s your starting point.