I don't have the card in front of me... but doesn't the helicopter lift say that is can be used at any time and that it doesn't count as an action?
Thus... yes the Pilot can do what you described. Also, the Pilot doesn't have to be the player with the Helicopter Lift card to be the one that is using it. .. any player can use their lift card at any time for any player.
... at least that's what I remember about the card.
Dave is precisely correct. Using a Helicopter Lift card does not count as an action, so it doesn't count as using the Pilot's special ability (which applies to the movement action) when used on the Pilot's turn.