A mortgage is a promise from the bank to gives you that money, so they create it.
Except that's not really what happens. Fully private banks can't just make money from a credit card loan (home loans are tricky because they have a real asset behind them). They have to have the deposit on reserve and if they don't then they borrow it from intrerbank lending. The Fed is the only one that creates money. The additional dollars from fractional reserve lending are real at each step.
Fractional reserve lending can (and likely has) been done with Bitcoin. Person A buys some bitcoin from Mt Gox and gives it to pirateat40. pirate then sells the coin at mt gox to get fiat to put into Zeekbucks. The person who buys the coins happens to be person A again, who sends pirate more money.
Ignoring the rediculous 7% interest, in the scenario above, Person A at one point in time has a single bitcoin twice. Once in their Mt Gox account, and twice as a note from pirate for redemption.