Yes, RANDOMNESS is a Scrabble word!

Letter values in Scrabble US: R 1, A 1, N 1, D 2, O 1, M 3, N 1, E 1, S 1, S 1.

Is it a valid word?

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

(thermodynamics) a thermodynamic quantity representing the amount of energy in a system that is no longer available for doing mechanical work
the quality of lacking any predictable order or plan

Also: s.

Not playable in Scrabble US: STOCHASTICITY.