In theory fractional reserve banking is possible however there are some unique constraints.
1) There is no central bank. Central banks also engage in FRB except they create the monetary base out of thin air. With Bitcoin the monetary base is fixed at ~21M BTC.
2) There is unlikely to be anything like FDIC. FDIC distorts the market in that the cost of insuring funds is paid for by taxpayers not depositors. While it is possible that in the future Bitcoin banks will exist and will even be insured it almost certainly will be private insurance. This makes using a Bitcoin bank more expensive than simply holding the coins yourself. Some people will still use banks but a smaller % than in most fiat economies.
3) The reserve ratio will likely be higher. Private insurance companies will be profit driven (not public policy driven) and smaller reserves means more risk.
4) As long as BTC is appreciating in value relative to other currencies demand for loans will be modest. Say you need to buy a car. You could get a $10,000 loan in USD (which are dropping in value making repayment easier) or you could get a 100 BTC (assume $100:1 exchange rate) loan (which are rising in value making repayment harder). Some people will choose to borrow in BTC but it will limit demand.
5) Less need for a bank. Without a bank (or bank like entity) it is very difficulty and costly to engage in commerce in USD. Imagine no PayPal, no credit cards, no prepaid payroll cards, no checking account, no direct deposit. Even routine things like cashing your paycheck to buy a game on steam becomes next to impossible. The utility banks bring drives deposits into the bank.
The effective money supply is Monetary Base * Money Mulitiplier.
In most FRB systems the central bank can influence both the monetary base AND the Money Multiplier.
In Bitcoin the monetary base is fixed (once all coins are minted) and the Money Multiplier is unlikely to be very large.
Imagine a hypothetical scenario where 30% of all Bitcoins are in Fractional Reserve Banks. The insurance company requires a 50% reserve. That means the money multiplier is 1 + 0.3*0.5 = 1.15. The money multiplier with no Fractional Reserve Banking at all would be 1.
Traditionally the money multiplier in the US has been roughly 2.5 to 3. This has crashed recently due to the recession (well due to Fed's policies) however a money multiplier to 2, 2.5 or 3 seems highly improbable in Bitcoin economy given the increased utility of the currency and the reduced utility of a bank.