No, it’s exactly the opposite.
Water weight is mostly tied up in the water associated with glycogen (primarily in muscles and the liver). Your body has up to about 2lbs of glycogen which binds 4-times its’ weight in water. So that’s a total of \~10lbs your body can swing on glycogen+associated water weight during a fast–your body uses up the glycogen in about a day or so.
Adipose tissue, which stores fat, has almost no water content at all (10-20% water content IIRC), which is incredibly small considering humans are made up of \~60% water.