It absolutely does not. A C++ structure is a much richer object: it can have custom copying, moving and assignment behaviours, it can have vtables, it has RAII, etc. That's the whole point about the "object model" in the article: C++ has it, C does not.

What I think you're trying to say is "a POD structure with no custom behavior is essentially identical in C and C++". That is mostly true, though if the struct contains a union, C++ has stricter UB rules (there might be other differences as well, but that's the one I can think of at the moment).

What I'm saying is that extern "C" has no effect on structure compatibility.