Is there any correlation? Short answer: No. Long answer: While there are types that are stereotyped as intelligent (Enneagram 5, Strong Logic in Psychosophy, Logical types in Socionics), as far as my research goes, there doesn't appear to be any correlation at all. It may sound counter-intuitive, but even frequency of thought does not translate to quality of thought. Just as airheads can have incredible thoughts and ideas, overthinkers can have nothing to flaunt. This phenomenon did puzzle me at one point, but I have long accepted it as the inescapable reality, even if I may not fully understand it.

However, while there is no correlation with actual intelligence, some types do perform better than others at imitating intelligence. Namely, Logical types in Socionics. It is my observation that a person of a Logical type can hardly ever be described as "smarter than they seem" because their systematic approach to information is already compatible with the common perception of an intelligent person, so they don't have issues in the department of imitation. On the other hand, Ethics types are better at performing sophistication, but not intelligence, because the latter implies that you actually need to sound logical and efficient, which would involve Logic functions. There is also a case to be made for Strong Logic in Psychosophy being better at organizing their thoughts and explaining difficult concepts in simpler and fewer words, and thus having an advantage in this as well, although it can also backfire as most people find more complicated and hard to grasp explanations 'smarter'.

Most people think of themselves as intelligent - it's the default. Intelligence is simply not valued in our society; it's far from the first quality most people look for in others and base their judgement on, so it is a rare thing to be insecure or tense about. Therefore, despite this quality not being accounted for in my methodology, any obvious gaps between actual intelligence, performed intelligence, and one's estimation of own intelligence, is something I pay attention to regardless, so this topic will come up from time to time.

I purposefully refrained from defining "intelligence" in this post because it is a multi-layered subject and there is no one true way to define it that isn't too abstract to be useful and at the same time doesn't exclude anyone prematurely. Everyone has their own idea of what it means, and when you do psychological analysis of someone, it's the other person's interpretation that matters, not your own.