How could Vasher become Drab, since he would have to give up his Big Breath to do so?
The Divine Breath can be hid. Essentially, you have to view yourself NOT as a god at all, using a very specific bit of mental gymnastics. As a Returned, your body changes based on how you see yourself. (This, by the way, is an indication that Lightsong was more pleased with himself than he ever let on.)
You don't lose your Divine Breath, but it does go into hiding, making you look like a normal person. But you're still Returned, and are consuming a Breath at one a week. If you give away your other Breaths, you retain this hidden one, but your body will still consume its own spirit if left to do so. So you still need a Breath a week to survive, and will die the week you don't get one.
I left this as an intentional place to explore the magic in the sequel, which I had planned to be writing (and posting on my website) by the time Warbreaker was out in stores. The WoT has diverted me, and so I feel bad, since this ends up being a confusing question that a number of readers have had. The hints toward how this is working are very difficult to find. (The biggest one is probably in the opening, where Vasher thinks about how he could reach the Fifth Heightening instantly, if he wanted to.)