In my experience, only a tiny bit dribbles out of the lines when disconnected. You will want to put some cardboard down to catch the drips (it drips out of the radiator tank as well).

Check the transmission fluid level when all is swapped over and pumped full. It must be a tiny tank in the radiator as I have never seen much of a drop in level after loosing the amount stored in the radiator tank. I would like to open one up some day and have a look.