Yes, ALLSPICE is a Scrabble word!

Letter values in Scrabble US: A 1, L 1, L 1, S 1, P 3, I 1, C 3, E 1.

Is it a valid word?

ALLSPICE is a valid word in the official Scrabble dictionary (US), the UK Scrabble Dictionary and Words with Friends (ENABLE).

aromatic West Indian tree that produces allspice berries
deciduous shrubs having aromatic bark; eastern China; southwestern and eastern United States
ground dried berrylike fruit of a West Indian allspice tree; suggesting combined flavors of cinnamon and nutmeg and cloves

Also: allspice tree, pimento tree, pimenta dioica.