Yes, and the weight remained the same because their was no change in mass that was contained within the truck. This should help answer the question about this myth as well. Standing on ones hands before stepping on a scale will not change ones weight.
First, the myth wasn't about the difference between the mass of the truck when the birds were in rest compared to when the birds were in flight, the myth was about whether the birds flapping their wings created some kind of "lift" that made the truck itself lighter.
That being said, the problem they eventually ran into with this myth is they couldn't make sure the birds stayed in the air the entire time with the fan that they used, and they had to use that style of fan at the speed they did because they couldn't use something bigger/badder without risking the lives of the birds.
How they eventually tested the "lift" theory (not the mass theory) was they built a helicopter and flew it in the truck, and it did not create this magical "lift" to make the truck lighter.
But in the end, the myth wasn't testing the mass of a closed system and the effects of the birds resting/flying around in that closed system, it was testing the myth that the birds flying around affected the weight of the truck itself. Which it did not.