Yes, DRAGGING is a Scrabble word!

Letter values in Scrabble US: D 2, R 1, A 1, G 2, G 2, I 1, N 1, G 2.

Is it a valid word?

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

pull, as against a resistance
draw slowly or heavily
force into some kind of situation, condition, or course of action
move slowly and as if with great effort
to lag or linger behind
suck in or take (air)
use a computer mouse to move icons on the screen and select commands from a menu
walk without lifting the feet
search (as the bottom of a body of water) for something valuable or lost
persuade to come away from something attractive or interesting
proceed for an extended period of time

Also: sweep up, drag in, get behind, hang back, drop behind, drop back, drag on, drag out.