I'm not sure how to respond to this. You're asking if Tesla had the power to see extra-dimensional structures? I guess I'm fairly secure in assuming that Tesla was experiencing hallucinations, in ways that are common among people experiencing hallucinations (unexplained lights are fairly standard), rather than possessing extra-dimensional superpowers that would, as far as we know, be completely unique to him.

Unless you're positing that anyone experiencing these types of symptoms are in fact viewing extra-dimensional objects. In which case, good luck with that.