Not in Iranians at least (that’s where the study was done). From Nutrition Journal:
Adherence to the low carbohydrate diet, which contains high amount of fat and proteins but low amounts of carbohydrates, was not associated with increased odds of psychological disorders including depression, anxiety and psychological distress. Given the cross-sectional nature of the study which cannot reflect causal relationships, longitudinal studies, focusing on types of macronutrients, are required to clarify this association.
I’d have been surprised if the researchers did find a linkage. But you don’t know for sure until y0u do the science.
Steve Parker, M.D.