I have had that thought for 20 years when I made the realization that the fear of stuttering in a situation would trigger the stutter to happen, so I even tried going to a hypotherapist to see if they could make me forget that I stuttered, news flash, that was a dumb idea, but I was desperate to try anything. Fast forward 20 years and the theory, at least for me, has actually held up, I have become fluent in 90+% of my day to day interactions and I feel like it's mostly because I've stopped thinking about it so much. So I think there is merit to the idea of the psychological side of it having a triggering effect to the physical side. However, I don't think that simply putting our anxiety into a fluent person would cause a stutter since there is an underlying physical phenomenon that creates the stutter/block that the fluent person probably won't have for the anxiety to trigger.