Mike
it's great that you are researching and trying methods like this to help with your tics and depression. Low carb diets are often associated with increased depression due to lowering of serotonin when there are insufficient carbs in the diet.

Just a word of caution....saying "Tourette's IS..... x y z" is a slippery slope.....once you get to know a cross section of people dx with TS you realize the syndrome is as variable as those who have it, and that many people who have been dx with it actually have other tic disorders caused by a whole range of variable things....

Both TS itself (which does seem to have a genetic component) and the numerous tic disorders are complex issues!

Hoping that for you, the dietary modifications are what is needed!