Yes they may try to partner with them as other means of transaction,but for me I will not like the Bank or the Bitcoin to have anything to do with bank ,because the bankers are not trustworthy, just take a look at our present situation now with the bankers,..

Allowing the bank to partner with the Bitcoin in terms of deposit will lead to the crash of Bitcoin because alot of things will go wrong.if bankers are involved in the Bitcoin deposits for a example:

1) people will lose interest in Bitcoin because they don't trust Bank anymore.
2) scamming Will increase because transactions with the Bank can never be as good and trusted like p2p
3) it can lead to involvement of politics.
4) hackers will come in
So I prefer  it the way it's now than involving bank deposit..