I have never removed a gland unless I am removing the whole hide, I do skin the deer as soon as possible. It is good for the meat as well as being easier to skin. It is the same with small game especially squirrels, skinning while warm is a whole lot easier!
I went on a hunt in NC and they would take the deer out, guts included, and pull the hide off with a winch working from the head back. Pretty slick operation when the deer is warm, not good if you are going for a mount.