Is it possible to take off on an elevated short field by "falling"?
Is it theoretically possible? Sure.
Is it realistic or probable? Absolutely not.



If there is not enough space for the airplane to accelerate to takeoff speed it will be effectively stalled when it reaches the end of the ground. That means that as soon as it runs out of ground it effectively becomes a ballistic projectile: it keeps moving forward, but it also starts to fall because of gravity. You can see this in the Goldeneye clip - the plane adopts a nose-down attitude shortly after it leaves the ground.  

Eventually, given enough time, the airplane will reach a flyable airspeed (between gravity accelerating it down and its thrust propelling it forward). How far it needs to fall before that happens depends on a number of factors, but if the ground is sloping downward at an angle such that the aircraft's ballistic trajectory does not intersect the ground before it can reach flying speed you could theoretically make such a takeoff.
The obvious downside is that if things don't go perfectly in the attempt you will intersect the ground in uncontrolled flight ("crash").



In the Goldeneye scenario the aircraft is already in a fairly extreme dive when Bond manages to get aboard, so for our intrepid secret agent it's not so much a matter of getting the aircraft to a flying speed (it's probably there already) but rather of recovering from the dive before hitting the ground and without over-stressing the airframe and causing parts to break off.