There are no guarantees, alas. However, the metabolic healing from a ketogenic diet has been known to accomplish amazing things.
The key benefit from a ketogenic diet lies in providing a different fuel source to our body. Instead of burning mostly sugar, with all the attendant damage that causes, we switch to fat and ketones, which are a much cleaner fuel.
Where mental illness and motor-neuron disease are concerned, a ketogenic diet helps because the brain can live almost entirely on ketones, and it doesn’t require insulin to absorb and metabolise them. With glucose, the story is different; insulin is required for brain cells to absorb it, but paradoxically, too much insulin hampers glucose absorption in the brain. So (a) a ketogenic diet lowers insulin throughout the body, and (b) ketones feed the brain even when glucose metabolism can’t.
So a ketogenic diet certainly won’t make your mental situation worse, and it may well improve it.
As for metabolic syndrome, it is basically the result of a state of hyperinsulinaemia and insulin-resistance. A ketogenic diet has been shown to be of great help in reversing the effects of metabolic syndrome throughout the body. No one can say for certain what benefits you can expect, but on the other hand, it is almost certain that you will notice improvements.