It might. Give people empty calories, take away the amino acids, vitamins, enzymes and other nutrients require for normal brain activity, and people get numbed and dumbed down, apathetic, weak.
I have always stood up to authority and as I have improved my health, my will power and energy to stand up to authority has increased substantially.
Very difficult to measure IMO - a causality analysis requires more control over the variables. It's too easy to make measurement errors in social psychology studies.
Who would be willing to eat fast-food and put themselves on a bad diet to test if their ability to resist authority deteriorates? The sampling bias alone would be too big and skews the whole result.
And people learn: Maybe their behavior in authority tests changed not because of their diet but because they get confronted with those tests more often. We can't be sure that they slept enough or that the food is responsible for their change in behavior.
Designing such a study and pulling it off without making major mistakes is harder than writing completely bug-free code for a big software project.