I don't think that would happen mostly because banks don't want to take bitcoin and adopt bitcoin anytime soon, I think bitcoins is a money of the future and the banks would also take BTC in the future but not now... I guess a bank could be profitable if it's giving profit in deposits "in btc".
Well it is not really going to happen unless the is going to make it as their business partner. But for me, banks are seeing bitcoin as a threat to their industry and I don't think that they are going to adopt it as the value of bitcoin doesn't have stable value and they are not going to adopt it as they are not certain about getting profit with it.