12. Ball not dead
The ball does not become dead on the call of No ball.
16. Out from a No ball
When No ball has been called, neither batsman shall be out under any of the Laws except 33 (Handled the ball), 34 (Hit the ball twice), 37 (Obstructing the field) or 38 (Run out).
© Marylebone Cricket Club 2013
As others have mentioned, if the laws had been followed to the letter, the batsman is out. However, no "Call" was made therefore it is understandable that the batsman may have set off for a run not realising that it was a no ball. Ball should be called dead.
EDIT: what I'm trying to say is that the only reason the ball is dead is because the laws of the game had not been followed for this delivery.