I don't know, I think if you are sick with a stomach problem (as I assume from you trying to settle your stomach), it's not worth it to be militant about the diet. No, it's not license to eat whatever you want whenever you want, and as soon as you feel better hop back on atkins. I do not see the harm in a few saltines or a piece of toast and broth if you can't stomach anything else.
However, if you just have a cold, then there is no excuse

I vote for being gentle with yourself when stomach-sick, keeping Atkins principles in mind as best you can.