Didn't start with a bank, didn't grow with a bank and I highly doubt it will need a bank in the future to survive.
I can say yes Bitcoins can survive without any bank or any financial institutions help. Because itself started its life cycle without any need of bank and that is the speciality of Bitcoins and its degital wallet.
How we deposit our fiat into online wallets as paypal?As i know we need banks to be able to credit our balance i dont know any other way,soo bitcoin without banks now its possible but hard,as we will have to work with others services like wu.