My thought is this: since fractional reserve banking basically creates money out of nothing,
It does not create money "out of nothing". Repeating the same false statement over and over again does not make it true.
The money that's finally created during the process of lending is created out of the opportunity value of the lent money.
wouldn't it be impossible to have such a system based on bitcoin?
No. In fact, as we speak, it's already happening and it has for quite a few years. It doesn't happen on a large scale, yet, though.
There will be a time when it starts to "get out of hand", though, and that will be when bitcoin is adopted by payment processors like e.g. paypal.
Imagine the scenario where paypal starts embracing bitcoin.
They won't require their users to transfer bitcoins into the paypal system before they can use it, but will rather make it possible for all their users at once to just use bitcoin like any other currency. I.e., you have a paypal account and want to buy something that's priced in bitcoins, paypal does the currency exchange for you and off you go. They will need a large stash of coins to do so but it will nowhere be near a 100% reserve for all their users' holdings.
Paypal is just an example here. The same would apply if banks let customers have accounts in bitcoins or with credit card companies, etc. pp., you get the idea.
If so, how would this effect bitcoin's potential as a global reserve currency (if it indeed has any)?
It doesn't. In fact, for a reserve currency, the same rules apply as for any other currency, so I don't see where there could be any problem.
Bitcoin could make a good reserve currency because its monetary base is directly electronically transferrable, which is not the case for e.g. the Dollar or the Euro.