No, but your compiler MIGHT decide in a future release that it's a whole lot faster to ignore the header files for standards types and definitions and just copy a pre parsed version of the struct into the symbol table when the header is included. It might look at the _t and decide nope, I don't have a definition for this so it's an error, despite your own definitions.
This probably won't happen. But if it does you don't have any grounds for complaint really.
The compiler to do that would also need to drop C standard compatibility (section 7.1.3 of C99). Which is probably a good reason to complain and to just stop using that version of this purely theoretical compiler.
This probably won't happen. But if it does you don't have any grounds for complaint really.