Yes, NAVY is a Scrabble word!

Letter values in Scrabble US: N 1, A 1, V 4, Y 4.

Is it a valid word?

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

an organization of military vessels belonging to a country and available for sea warfare
a dark shade of blue
the navy of the United States of America; the agency that maintains and trains and equips combat-ready naval forces

Also: naval forces, dark blue, navy blue, united states navy, us navy.

Not playable in Scrabble US: USN.