I think the price of bitcoin will not affect the fiat. Fiat will stay the way they are, and if the price of bitcoin reach $10.000 i think many people will start using bitcoin. Realy can't for image the on the day.
I think it's just the other way round, first more people start using Bitcoin and then the price of it rises to $10k or whatever. IMO $10,000 for 1 Bitcoin is not that unrealistic as it may look. I think this might happen when 20 times more people than now will be using Bitcoin (probably a matter of 2-3 years).
I don't think that price can be achieved in next 3 years, its taking long time even to cross $1k so I think it will take more then 10 years to achieve that price but no one is confident about it.