Take for example the case of people who have never seen from birth and are given sight through retinal implants; they can see colours and images and patterns but their brains can make no sense of the input - they sense no depth, shapes, relations between words and images, shadows meaning three dimensionality, etc. etc. that we all take for granted. Those neurones have been put to alternative use already and in some ways you really can't teach an old dog new tricks.
I’d imagine any such system would have a learning curve as each brain figures out the patterns but it seems there isn’t any fundamental difference that makes each person’s thoughts unintelligible.
(Granted, as siblings one could argue their thoughts would naturally tend toward being intelligible but it seems too early to know the answer to that question)
While it may be possible to learn and figure out patterns from someone else that you were connected to, I think it would be immensely difficult. You may have to learn the whole world from their point of view from scratch for any mental relations they communicate to have any meaning.
Similarly, we serialize our internal representations into language for - literally - serialization. It's for transmission, but also allows differing internal representations.