Nu-uh.
According to wikipedia:
In botany, the berry is the most common type of fleshy fruit in which the entire ovary wall ripens into an edible pericarp.
The watermelon is a pepoe (beats the hell out of me) - but what i did find is:
Vampire pumpkins and watermelons are a folk legend from the Balkans, in southeastern Europe, described by ethnologist Tatomir Vukanović. The story is associated with the Roma people of the region, from whom much of traditional vampire folklore, among other unusual legends, originated.
The belief in vampire fruit is similar to the belief that any inanimate object left outside during the night of a full moon will become a vampire. According to tradition, watermelons or any kind of pumpkin kept more than ten days or after Christmas will become a vampire, rolling around on the ground and growling to pester the living. People have little fear of the vampire pumpkins and melons because of the creatures' lack of teeth. One of the main indications that a pumpkin or melon is about to undergo a vampiric transformation (or has just completed one) is said to be the appearance of a drop of blood on its skin.