The main difference between a fractional-reserve BitCoin bank and a conventional bank would be that there would be no lender of last resort to use in case of a bank run.
Other than that, you'd still fulfill the basic function of creating liquidity -- any individual depositor has full access to their money, and your creditors also make use of it, so the money supply increases.
Just because there's no BitCoin-denominated lender of last resort also doesn't necessarily screw you in case of a bank run. If your loans are sound, any individual bank could probably find lenders in case of a run: if all of a banks depositors want their BitCoin back at once, the bank would go to other banks or lenders and borrow BitCoin against the value of their loans. As long as there is sufficient liquidity in the entire banking system, the individual banks could survive a run.
You could also get around the lack of a BitCoin-denominated lender of last resort by using a non-BitCoin-denominated lender of last resort: while the accounts may be BitCoin-denominated, you could (in the ToS) give the depositors an equivalent amount of USD if you "run out" of BitCoin and you are unable to borrow BitCoin from other lenders. It'd be more complex because you'd need to borrow USD against the value of the BTC-denominated loans you yourself have, and then insure against the risk of a BTC crash, but that's the sort of think that financial and insurance people do all the time.
Other than that, you'd still fulfill the basic function of creating liquidity -- any individual depositor has full access to their money, and your creditors also make use of it, so the money supply increases.
Just because there's no BitCoin-denominated lender of last resort also doesn't necessarily screw you in case of a bank run. If your loans are sound, any individual bank could probably find lenders in case of a run: if all of a banks depositors want their BitCoin back at once, the bank would go to other banks or lenders and borrow BitCoin against the value of their loans. As long as there is sufficient liquidity in the entire banking system, the individual banks could survive a run.
You could also get around the lack of a BitCoin-denominated lender of last resort by using a non-BitCoin-denominated lender of last resort: while the accounts may be BitCoin-denominated, you could (in the ToS) give the depositors an equivalent amount of USD if you "run out" of BitCoin and you are unable to borrow BitCoin from other lenders. It'd be more complex because you'd need to borrow USD against the value of the BTC-denominated loans you yourself have, and then insure against the risk of a BTC crash, but that's the sort of think that financial and insurance people do all the time.