I think it's a bad analogy for many reasons. First and foremost, birds do not leap a mile up into the air. Birds lift themselves off the ground with their wings, not with their feet. This alone invalidates the analogy. The gun generates all of the force needed to propel the shell a mile upward in a short period of time, and does so with a rigid connection to the truck floor. For a mortar with a 1 meter barrel (the 177.7 m/s muzzle velocity does not need a long barrel) and a smallish 8 kg round, the gun expends about 250,000 newtons of force over a 10 millisecond interval, nearly an order of magnitude larger than the weight of a typical 16 foot truck. Birds generate lift by flapping continuously. The force applied by birds to loft themselves extends over a much longer period of time. The medium through which the birds apply the force to loft themselves is loosely coupled with the truck floor. The gun operates in a vacuum. Birds do not. The downward deflection of air is critical in explaining how birds fly. The "birds in a truck problem" implicitly asks for the steady-state solution. The steady state in the gun situation is the ballistic trajectory. The truck will weigh less while the shell is flying than it did before the gun is fired. Once the birds achieve level flight the truck will weigh more-or-less the same that it did before the birds took off, with some small deviations that result from the birds' flapping. When you change too many aspects of the problem the analogy becomes a false analogy.