Yes, DRUNKENNESS is a Scrabble word!

Letter values in Scrabble US: D 2, R 1, U 1, N 1, K 5, E 1, N 1, N 1, E 1, S 1, S 1.

Is it a valid word?

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

a temporary state resulting from excessive consumption of alcohol
habitual intoxication; prolonged and excessive intake of alcoholic drinks leading to a breakdown in health and an addiction to alcohol such that abrupt deprivation leads to severe withdrawal symptoms
the act of drinking alcoholic beverages to excess

Also: alcohol addiction.

Not playable in Scrabble US: CRAPULENCE.