No. Water expands when it freezes and tends to break through the cell walls of fruits, vegetables, and meats that have a high water content or a delicate cell structure. And as you well know, watermelon is about 138% water and has a very delicate cell structure. If you freeze a watermelon, the only thing you'll wind up with when it thaws is a mushy pulp. A pretty pink pulp. With seeds.

Plus, think of the space it would take up in your freezer. Some foods are meant to be enjoyed when they are in season, and that's all there is to it.