No, Bitcoin will not replace Dollars. Bitcoin only will be a secondary payment option since most of people in the world even dont know to operate a computer in developing countries.
Bitcoin has already replaced dollar in the deal of worlds most expensive pizaa so there are many bitcoin users who prefer bitcoin over dollar or other fiat currencies but I dont think bitcoin will vanish the dollar or any other fiat currency. On individual level, bitcoin has already replaced our fiat currencies (at least online).
That pizza story gets a lot of attention, but it's not an accurate way to think about it. At the time that guy bought the pizza, those bitcoins were only worth the price of a pizza. It wasn't a million dollar pizza. It's the same thing as looking at a gambling website that had 1000 bitcoins wagered on it when Bitcoin was only worth $200. The value of the wagered amount is $200,000. A couple years later, if Bitcoin is worth $1000 each, it's not accurate to say that the website has had $2,000,000 wagered on it, cuz the amount wagered was only $200,000 at the time.