Nah, the amount of snow and ice on land like in Antarctica is extremely small to the amount of water in the sea, especially since it needs to expand outward and cover even more land.
With thermal expansion even only being a clouple of % is enough to rise everywhere multiple meters. Which is nothing compared to the +10km of dept at the Mariana Trench.
Of course, all of it adds together in the end. It will be bad for everyone no matter where it comes from.