Yes, DESPERATE is a Scrabble word!

Letter values in Scrabble US: D 2, E 1, S 1, P 3, E 1, R 1, A 1, T 1, E 1.

Is it a valid word?

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

arising from or marked by despair or loss of hope
desperately determined
(of persons) dangerously reckless or violent as from urgency or despair
showing extreme courage; especially of actions courageously undertaken in desperation as a last resort
showing extreme urgency or intensity especially because of great need or desire
fraught with extreme danger; nearly hopeless

Also: do-or-die.