No, I think that it can't. It could be used along with traditional money but it can't entirely replace it. Unfortunately bitcoin has to many issues, weeknesses and characteristics that don't allow it to be fully used and implemented in traditional financial system. Volatility is just one of them.
Bitcoin can be used together with the fiat for now because bitcoin also need the value of money to develop. I also do not think that bitcoin can replace fiat for transaction it can either be a option for people on doing their transaction. Because the legal matters of fiat is much trusted because the stock is on the government hands. But bitcoin may develop also for more changes that may lead for more people to chose bitcoin than fiat in doing transaction on a daily basis.