Yes, SQUASHY is a Scrabble word!

Letter values in Scrabble US: S 1, Q 10, U 1, A 1, S 1, H 4, Y 4.

Is it a valid word?

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

like a pulp or overripe; not having stiffness
(of soil) soft and watery
easily squashed; resembling a sponge in having soft porous texture and compressibility

Not playable in Scrabble US: SPONGELIKE.