It would be an interesting strategy but I think it overlooks the importance of the phrase, in Article 50, that leaving should be "in accordance with the member state's constitutional requirements". It would be quite clear that a PM refusing to obey the law in an attempt to force leaving would have failed to act in accordance with our constitutional requirements, and I am sure that the EU would accept that Leaving on those terms had not actually happened in spite of the time allowed having elapsed.
Besides, even if the PM sat tight, the wheels of law can move very quickly indeed if it is judged necessary. As two cases in point, the Withdrawal (No 2) Act took six days to go through all its stages, while the Supreme Court heard and ruled on the prorogation case in a week. In a genuine emergency I wouldn't be surprised if the necessary legislation, at least, were passed inside a day wih the cooperation of both Houses. And, since the context would be a Prime Minister breaking the law, I doubt that there would be much opposition to that speed.
This is all hypothetical, of course, and yet to be tested. But, following on from my post(s) in a separate thread from last night, it also supposes that Johnson's aim is to deliver Brexit. It is almost certainly not. Johnson's aim is to paint himself as a hero if he succeeds and as a martyr if he fails, and use either of these positions as the pitch in the snap Election. In that regard, Johnson's insistence on leaving on October 31st is posturing rather than actual intent.