Yes, shad is in the scrabble dictionary

...and is worth 7 points by itself if you played it.

Shad Definition

noun

Any of several food fishes of the genus Alosa, especially the North American species A. sapidissima, related to the herrings but atypical in swimming up streams from marine waters to spawn.
Any of several fishes (especially genus ) of the herring family that differ from the typical herrings (genus ) in having a relatively deep body and in being anadromous and that include some important food fishes of Europe and North America.