The real question is how much can the system pay-out? Bank's can't pay everybody their money in cash/gold; can't imagine the Bitcoin generating exchange mecanism has the money behind it to cash out everyone who wants to either. Or can you only get out if someone gets in?
This is true for all transactions, though. There isn't anywhere NEAR enough cash and gold in in the world for everyone to cash out of real estate, or the stock market, or even their checking accounts. Yet all of those things still have value.
This is the great mystery of the modern financial system. It's all based on debt. Your checking account doesn't have money in it, it has debt in it. Debt that the bank owes to you in exchange for you giving them cash up front, but they have of course already spent that cash somewhere else.
I get up and go to work. My employer issues me an electronic paycheck (they create debt to me) which is deposited into my electronic bank account (which becomes bank debt to me in exchange for my employer's debt to me). I buy goods and services with a credit card (I create debt to the cc company) and then I pay the cc bill electronically (I transfer the bank's debt to me to pay off my debt to the cc company). At no point in this cycle is there actual "money" involved, just promises and IOUs, and yet it drives the entire engine of our economy on both the production and consumption sides. Debt IS money, because it is spendable and transferable. The amount of cash in circulation is far far less than the amount of money/debt in circulation, which is far far less than the amount of "wealth" stored in fixed assets like real estate.
Everything is a market. Everything has a market price at any given moment that is determined by what the financial system can pay for it. Gold doesn't matter. Cash doesn't matter. All that matters is liquidity and control of debt. Realizing this is what allows people like Donald Trump to become billionaires without having any actual money of their own. They just find ways to exchange debt, no actual capital required.
But it can all come crashing down at any time, of course. We've seen it before and I'm sure we'll see it again.