The answer is yes according to some recent studies reported by Doug Gross on CNN, Experts: Most people will make purchases via phones by 2020. He reported that nearly two out of three respondents to a (65%) Pew Internet & American Life Project survey that most people will have fully adopted the "mobile wallet" as their day-to-day means of paying by 2020. This leaves 45% as doubters. Doug added that, “in a December report from comScore, 38% of smart phone owners had used their phones to make a purchase of some kind.”
There are obvious security questions but the article that smart phone technology is no less secure than the current credit card technology. In some ways it might be more secure it does not leave a physical paper trail. I was recently overseas for a while and turned off my smart phone so I would not getting any calls from the US that might be expensive. I missed the ability to play music and share pictures. I am sure there must be a way to use the phone for these non-telephone purposes while the telephone part is turned off.
I can see the utility of this as my smart phone has reduced the number of other device that I have to carry around. However, I do not think it will ever replace a wallet just as credit cards have not replaced cash. It will likely cut into credit card use but not replace it. Just as there are cash only signs at stores, there maybe cash and card only signs depending on how they handle the service fees to merchants. It will be interesting to see what happens. 2020 is not that far away.