Yes, ENGAGEMENTS is a Scrabble word!

Letter values in Scrabble US: E 1, N 1, G 2, A 1, G 2, E 1, M 3, E 1, N 1, T 1, S 1.

Is it a valid word?

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

a hostile meeting of opposing military forces in the course of a war
a meeting arranged in advance
a mutual promise to marry
the act of giving someone a job
employment for performers or performing groups that lasts for a limited period of time
contact by fitting together
the act of sharing in the activities of a group