Does mental health have anything to do with how smart you are?

Yes it does but - Maybe in ways you may not have thought. Understanding problems may come more readily and so may solutions because you are quick to get the ideas that mental health diagnosis and treatment are based on. That makes sense. What doesn't make sense is how many very intelligent people have mental disorders and either don't know it or believe they are immune to such a thing & don't do anything about it.
NO. No there is not a connection between mental health and intelligence.