From Rule 4:
SECTION 42 THROW-IN, THROWER, DESIGNATED SPOT
ART. 1 . . . The thrower is the player who attempts to make a throw-in.
ART. 2 . . . A throw-in is a method of putting the ball in play from out of bounds
Hmm, interesting question. When I look at the above, it seems to me-
1) The throw in has not ended
2) The player is attempting to put the ball in play from out of bounds
3) By definition, that player is now a thrower
So I would say, the language backs up your conclusion quite nicely.