Possibly for the cross country phase but I would say stadium is out and dressage is a definite no. As was pointed out the tail isn't braided in dressage anyway and in stadium I would braid, or, given that stadium is jumper style, leave the tail loose. You can spray it down with something like show sheen to help repel or keep the dirt from sticking.
Here is a much neater style tail knot that polo horses and field (for lack of a better term) hunters (foxhunters) use. Pro Equine Grooms - The Mud Knot