I didn't vote in the poll because there wasn't an option for "Yes, but with very different results than in the fiat world". As far as countryfree's comment that you could still get a mortage with bitcoin banks - yes, this is probably true. But forget about the 3% interest rates that you're seeing today (at least in the states), or even 5%. It'd probably be at least 15%.
Would credit be possible with bitcoin? Yes, but it'd be more difficult, and therefore likely much more expensive in terms of interest rates.
But why would it be more expensive? Bitcoin's nature is deflationary (after the initial inflation period), so it would make sense for bitcoin denominated interest rates to be
lower than fiat rates, because the interest rate does not have to overcome the inflation rate.
Quite - and I think this will be the problem for a bank that issues bitcoin-denominated liabilities (i.e. takes bitcoin deposits).
Recall: the purpose of a bank is to perform maturity transformation: it issues short-dated liabilities in order to fund positions in longer-dated, higher-yielding assets. The spread funds the bank's operations, covers losses and provides a source of profit. This makes banks inherently unstable and vulnerable to runs, which is a problem in and of itself in a world without a lender-of-last-resort that can print currency on demand to lend to solvent (but illiquid) institutions.
However, the bigger problem to my mind is that this model implies an institution that issues bitcoin-denominated liabilities must invest in assets that yield more than the yield they are promising their bitcoin depositors.
Now, if bitcoin's deflationary nature kicks in and the purchasing power of a bitcoin increases over time, the real challenge for the bank is to find suitable assets in which to invest.
If the only suitable assets provide a (real) yield of, say, 5%, it is entirely likely a bitcoin bank would have to offer nominal interest rates to depositors that are negative.
That can still be desirable in a fiat world since large holders of currency may not want to take responsbility for the safekeeping of physical cash (nominal yield 0%) and so would be content to accept a small negative nominal yield... but all Bitcoin users have the ability to manage their own wallets, at least in principle.
So... it's hard to see how someone could build a viable business model based on paying interest on deposits...