Yes. But these live traps come in all kinds of sizes, so speculating won't help much. I have brought 3 adult birds, a trio, in a large trap with no issues. I typically make a trip down to KY and back three times a year, and I am almost always hauling birds down and back. I have a couple of travel boxes that keep them secure and comfortable. The trip is 12 hrs each way, so I don't load them until I am almost ready to go. They do just fine if they have been fed and properly hydrated before hand.
In spring and fall, there's little issue, but in the summer? Absolutely travel only after sunset or arrive at your destination before noon. The hot afternoon is far too brutal for transporting birds. BTW, they poop a lot and they reek!!! I only carry them in the bed of my truck or in a trailer. One time and one time only in the back of the SUV. Ahhhhhh, nope never again.