A 1000-kg truck carrying 500 kg of live pigeons in a sealed cargo compartment pulls up to a weighing...

Problem

A 1000-kg truck carrying 500 kg of live pigeons in a sealed cargo
compartment pulls up to a weighing station; if the pigeons fly, can
drilling a couple of holes in the compartment reduce the weight?

A 1000-kg. truck carrying 500 kg. of live pigeons pulls up to a
weighing station.  It turns out that the truck is slightly overweight.
Wanting to bring the weight down, the driver bangs on the side of the
sealed cargo compartment to get the pigeons to fly in the air.  (The
compartment is 2.5 m. x 10 m. x 4 m.)

But then she remembers she tried this once before and it didn't work.
Something about the truck's being a "closed system".  So she goes to
the glove compartment and gets out a battery-operated drill with a 1/4
inch bit.  "I'll drill a couple holes into the compartment," she
reasons.  (Two holes are all she can drill before the battery gives
out.)  "Then the air inside will become an extension of the outside
air; the pigeons will be supported by the atmosphere, not the truck;
and the truck's weight will fall to 1000 kg."

Is she right?  Can she affect the truck's weight at all?  Where should
she put the holes (if it matters)?  What are the consequences for the
pigeons?

(Thanks to the Oracle, in the person of D. W. Ring, for helping with
the quantitative end.)

-- Pete Kimball

[ Editor: the first paragraph is the editor's summary. ]