Maybe. I'm no aeroE, but I know parachutes need a reasonable bit of space to deploy. I'm not sure the quadcopter would be flying at a high enough altitude to be able to deploy the parachute, have it unfurl properly, and then contribute enough drag to slow the craft.

Also, it'd mean either parachute or this failsafe rotation technique. Spinning freakishly like the video shows would only get the quad entangled with a parachute.