Is it possible to throw caged animals into a pit without connecting each cage to a lever? When I try to assign the animals to a pit, they break loose from their cages as soon as a dwarf start dragging.
The answer is a resounding... "kinda".
What you want is a cage that's as close to the pit as you can get it. Dwarves have a tendency to freak out over any non-tame animal, but sometimes if they are close enough, they'll transfer the animal before they freak out.
Case in point: I once had a caged fox that I wanted moved into a built cage. I stationed my military dwarf between the two cages and prepared for the worst. A dwarf came by, unlocked the fox, began to panic, and ran away. My unarmed military dwarf immediately started wrestling with the fox, when all of a sudden, a 2nd civilian dwarf, responding to the original job request, grabbed the fox mid-battle and threw it into the proper cage. My military dwarf continued to stand outside the cage and glare at the fox.
In short: Dwarves are crazy. Sometimes nearness helps, sometimes it doesn't. (And never, ever, try and sell your bronze colossus cage.)