Two possibilities:
According to James Rickards, gold is going to be worth $10,000 an ounce of gold (today USD 1.3k). If Bitcoin reaches $10,000, I'd say the catastrophe would be even bigger. Fiat almost worthless.
OR
The financial bubble we are experiencing today gets so big that bitcoin 16-folds its current price, and the same happens to every other asset (not necessarily in the same magnitude. Fiat almost worthless.
Final result: Yes, fiat would be worthless.
I do not think so. If the bitcoin is even $1m, it is just less than about 10% of the world currency usage, the rest will be fiat.