Yes, TUMBLER is a Scrabble word!

Letter values in Scrabble US: T 1, U 1, M 3, B 3, L 1, E 1, R 1.

Is it a valid word?

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

a gymnast who performs rolls and somersaults and twists etc.
a glass with a flat bottom but no handle or stem; originally had a round bottom
a movable obstruction in a lock that must be adjusted to a given position (as by a key) before the bolt can be thrown
pigeon that executes backward somersaults in flight or on the ground

Also: tumbler pigeon.