Yes, EUCARYOTE is a Scrabble word!

Letter values in Scrabble US: E 1, U 1, C 3, A 1, R 1, Y 4, O 1, T 1, E 1.

Is it a valid word?

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

an organism with cells characteristic of all life forms except primitive microorganisms such as bacteria; i.e. an organism with `good' or membrane-bound nuclei in its cells