Yes, PUSHUP is a Scrabble word!

Letter values in Scrabble US: P 3, U 1, S 1, H 4, U 1, P 3.

Is it a valid word?

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

an arm exercise performed lying face to the floor and pushing the body up and down with the arms

Also: press-up.