No I do think this can happen in my opinion this is highly unlikely but we will see what is gonna happen of course because the fact is that its not to predict.
The banks are controlling the world and they have a lot of power that is why I do not think the bitcoin do it.
But banks have always found a way to adopt to the latest technologies and surely if the bitcoin becomes more and more popular and more investments were put into it, they will defiantly adopt and start using it as well, many online banks are starting to go down that road since a lot of the online freelancers use bitcoins.