I have never heard anything about this but it sounds like a bad idea. I would just drink water and keep it simple. The extra gas from the carbonated coke could make you feel even worse.
You do have a good point when it comes to gas. At the same time too it sounds like the benefits may outweigh the risks here at the same time too. I can understand how Coke might be able to eat right through what food is stuck in your pouch if it's powerful enough to dissolve rust at the same time too. Right now I'm drinking Key Lime Sparkling Water which isn't giving me any noticeable problems. So far my liquid only diet today has been harmless. I still haven't digested any Diet Coke though. I really don't like drinking Diet Coke solo, I really like it to be accompanied with food.