You also lose a significant amount of weight. Think about it this way: some birds (like vultures) evacuate waste before returning to flight because it makes them lighter.
Why would it be different for any other animal, unless such a thing puts them at a significant disadvantage? Human urine is sterile, so a predator would be able to safely eat a person even if they pissed all over themselves provided that their waste hadn't contaminated their flesh (which it wouldn't). If anything, the scent of human urine would make them easier to track, but lighter and more comfortable in the process of fleeing.