Yes, DIVULGED is a Scrabble word!

Letter values in Scrabble US: D 2, I 1, V 4, U 1, L 1, G 2, E 1, D 2.

Is it a valid word?

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

make known to the public information that was previously known only to a few people or that was meant to be kept a secret

Also: let on, bring out, give away, let out.