I think a pass remains a pass even if it is batted.  Sometimes you hear a pass being incomplete when it's batted down.  But further down on this page, I recalled that a pass was batted up in the air in the end zone, and the quarterback was able to get to the ball and bat it out of the end zone.  And I recall that Roger Staubach (still playing for Navy?) had a pass batted up in the air; he caught it, threw it again, and drew a penalty call for throwing that 2nd pass.