Yes, I figured Doohan was probably pulling our collective leg with that “future Scotsman” remark.
Even so, it's not without merit. Accents really do evolve over time. The Scottish accent of today would probably be unrecognizable to a Scot from 300 years ago, and so it stands to reason that a Scottish accent 300 years from now would be rather unlike the present one. Same with a Russian accent like Chekov's.
People sometimes complain about the Frenchman Jean-Luc Picard having an English accent. My response is, who's to say that isn't what a French accent will sound like 400 years from now?
Certainly true. If you listen carefully to Jimmy Doohan's attempt at a burr, he definitely gets some
of it right - just as accents/dialects today undoubtedly retain some of what they sounded like in centuries past.