In this generation, nothing is ever impossible with the economy. There is always a possibility to banks offering bitcoin deposits. In some countries, there are bitcoin machines for withdrawals. So if it will be spreading to other countries, the banks may be pressured to offer deposits. Bitcoin is almost accepted everywhere so there's always a chance for anything.
Banks will eventually do the same what Telecommunication companies are doing right now by providing internet services as there is no longer use of call and sms packages because of whatsapp and facebook. same will be the case with banks. if they are not gonna offer bitcoin deposits, they will ultimately do something to provide services related to bitcoins.