I wouldn't put caulk anywhere that the pigs might be able to chew/ingest it.
What type cage are you building? If you are building one of the C & C cages with a coroplast bottom, there is no need for caulking. If you really want to make sure it is sealed I supposed the caulk would be ok as long as you used it on the outside of the cage. You could try just running duct tape along the seams too....walmart sells it in different colors now.
