I am not quite sure that I understand how a Bitcoin bank would operate. I am under the assumption that banks would lend Bitcoins and not USD;
yes
Let us say that: a bank accepts deposits and receive 1000 Btc from various depositors. They give loans, but owing to the fact that they do not have Btc or rather the codes that Btc are made up from, they can never lend more than 1000 Btc. If the bank lends 1000 Btc no depositor can withdraw any Btc; which means that 1000 Btc equals 1000 Btc and not 2000 Btc.
there is no need to make it even more complicated and introduce interest rates in your scenario.
if my post wasnt intelligible read this:
http://en.wikipedia.org/wiki/Fractional-reserve_banking#Example_of_deposit_multiplicationreplace "central bank money" with "21 million coins" there and you'll have what a bitcoin bank can do.