Your example assumes that the ice is in the water already. Sea ice melting never has been behind concerns of sea levels rising. The concern about sea level rise was from:
1) Ice sheets and glaciers melting (ie, the ice that is on land in Greenland, Antarctica, etc - not ice that is in the water already) - that ice isn’t currently displacing any water, so any portion of it that melts will add to sea levels unless offset by higher precipitation (and retention of said precipitation) elsewhere on land.
2) Thermal expansion. Heat water by 5 degrees celsius and you’ll get about a 0.1% increase in volume. So for a 1 degree celsius change, that’s about 240,000 cubic kilometers of increased volume. Over 360 million square kilometers of ocean, that’s about 0.67 m of additional depth (neglecting the fact that surface area would increase).
Regardless of what you think of the theory of global warming, your example is pretty far off from fact. You don’t need extraterrestrial water sources - heat will in fact expand water, and melting of ice on land will result in higher sea levels.