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.