Yes, IMPULSIVE is a Scrabble word!

Letter values in Scrabble US: I 1, M 3, P 3, U 1, L 1, S 1, I 1, V 4, E 1.

Is it a valid word?

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

proceeding from natural feeling or impulse without external stimulus
without forethought
having the power of driving or impelling
determined by chance or impulse or whim rather than by necessity or reason
characterized by undue haste and lack of thought or deliberation; (`brainish' is archaic)