The only cost of getting the helicopter without cheats on Playstation 2 is to suffer the failure of the mission; however, I have found a way to succeed off the mission after getting the helicopter without cheats. Here is what you do as soon as you obtained the helicopter, you immediately fly over to Shoreside Vale until you get passed the welcome screen. At this point, notice that those two cars aren't moving at all on the map and the scale (I believe that once you go over to another island every moving object on the last island will stop and even the same case applies during the mission). Then fly over to the blue building back from the Staunton Island, where it is the destination point of where all these celebrities are heading for in the mission. As soon as you fly over there, quickly made a landing in front of the building and wait for those two celebrities to arrive. Upon their arrivals, they will get off the vehicles to enter the building, and this is where you go dispatch them quickly before they can reach to the entrance of the building. That's how you do it.
Now you can obtain the helicopter without cheat and on the same token, complete the mission within one try! Neat huh!