It's an interesting connection, but as with all these gut-studies, I feel that there is clear correlation without causation. Stress leads to stuttering and stuttering leads to stress. Both can result in bad gut, but it's very hard to prove that bad gut will directly result in stuttering. I think there are way more people with gut problema than those who stutter, for example. Interestingly, my gut is also very reactive, which has made me quit coffeine and lactose-rich products, but I feel that it has no effect on my speech whatsoever.