Factional reserve banking based on Bitcoin is perfectly possible and will not increase the amount of existing bitcoins (although it will increase the money supply in a broader sense, with money equivalents).
But I don't think that this is what you are talking about. You are looking for proof of solvency of the exchanges. I don't think that this is possible. Sure, they can provide proof of reserves - but there is no way to prove that these reserves are exactly equal to the funds deposited by their clients.
If you audit them or they give a serial number for each account and a public list of the btc held by each account everyday so you can check if they control addresses corresponding to the total of bitcoins or more and each client can check if his number is right.