Yes, LARGENESS is a Scrabble word!

Letter values in Scrabble US: L 1, A 1, R 1, G 2, E 1, N 1, E 1, S 1, S 1.

Is it a valid word?

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

the capacity to understand a broad range of topics
large or extensive in breadth or importance or comprehensiveness
the property of having a relatively great size
the quality of being pretentious (behaving or speaking in such a manner as to create a false appearance of great importance or worth)

Also: comprehensiveness.