Yes, SYMPATHETIC is a Scrabble word!

Letter values in Scrabble US: S 1, Y 4, M 3, P 3, A 1, T 1, H 4, E 1, T 1, I 1, C 3.

Is it a valid word?

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

of or relating to the sympathetic nervous system
expressing or feeling or resulting from sympathy or compassion or friendly fellow feelings; disposed toward
showing or motivated by sympathy and understanding and generosity
(of characters in literature or drama) evoking empathic or sympathetic feelings
having similar disposition and tastes
relating to vibrations that occur as a result of vibrations in a nearby body

Also: good-hearted, large-hearted.