The bitcoin block chain at a low level is basically two things: it's an eternity service and also a timestamping and race-resolving service.  And as such it can be used as a public communication channel.  It is possible to layer additional protocols on top of it, and although it is far from ideal, it is possible.

Implementation details aside, at the core, you are establishing a system of deposits and withdrawls and transfers between account holders.  That part is not particularly problematic, but treating the deposits as if they were a new currency does not fit very well because the deposits are not at all cash-like.  The deposits cannot be transferred without the participation of the deposit holder, so they are more like checking accounts.

Now in addition, if the 'bank' establishes an understanding that accounts will be held in some asset other than bitcoins (gold, let's say), then that could be a benefit to account holders who don't want to be exposed to the risk of bitcoin value fluctuation.  It would be incumbent on the bank to properly position their assets rather than gamble with the account holders' money, but that's up to them.


The implementation details are not great, but it is doable.

Asking an institution to hold value in something other than bitcoins is not unreasonable.  The exchanges do it after all.

But if it is not cash-like, then I don't see a lot of point to integrating it so heavily with the block chain.  Since a central institution must be involved anyway, why not simply register a key with the bank and sign checks that transfer value from your account to another account?  All of the accounting and double-spend checking has to be implemented by the bank regardless, so the advantages of the block chain are really not being used.  Even a public, synchronized communication channel is not necessary.