Yes, SHEEREST is a Scrabble word!

Letter values in Scrabble US: S 1, H 4, E 1, E 1, R 1, E 1, S 1, T 1.

Is it a valid word?

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

complete and without restriction or qualification; sometimes used informally as intensifiers
not mixed with extraneous elements
very steep; having a prominent and almost vertical front
so thin as to transmit light

Also: out-and-out, right-down, gauze-like, see-through.

Not playable in Scrabble US: VAPOUROUS.