Theres a similar question to this in this months FHM believe it or not - so obviously the answer was 100% correct
!?!? The only difference being that the example used a truck rather than an aircraft. The answer that was given was that if the birds were all flying, a truck would indeed weigh less if placed on scales . Some people claim that the force of the air pushed down by the birds' wings counteracts the loss of weight imparted on the base of the truck by the birds - but this is blag because the weight of each bird is being supported by the lift in it's wings (roughly) and not imparted onto the a/c and downforce through bird wings compared to a/c lift is negligible. (I'm sure someone will give you a better, more detailed explanation including Newton's Laws of why this is not the case !). Therefore for straight and level flight I reckon the lift would simply have to equal the empty weight of the a/c. Of course I'm probably completely wrong and someone will correct my incredibly poor logic and reasoning !! But hey...