Yes, COMPLETENESS is a Scrabble word!

Letter values in Scrabble US: C 3, O 1, M 3, P 3, L 1, E 1, T 1, E 1, N 1, E 1, S 1, S 1.

Is it a valid word?

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

the state of being complete and entire; having everything that is needed
(logic) an attribute of a logical system that is so constituted that a contradiction arises if any proposition is introduced that cannot be derived from the axioms of the system