I feel like "make physically unwell" here just means they'll taste something gross, not realize it is the baking powder, and treat the feeling as if something is wrong with their body. I know mixing up baking soda and baking powder has made for some pretty unpleasant tasting food for me.
Yes, which is why it's easy to then convince people to evacuate. People do die on Everest, including EBC treks from altitude sickness alone, so severe symptoms usually lead to taking the trekking back down the mountain.
Baking powder is used by some athletes as it is shown to enhance performance.[0] I find it more realistic that they are adding it for that effect than making anyone unwell. As its not really something that makes you ill.