No, you have to keep either coins or cash on deposit with an exchange in order to trade. The smart thing to do is not store your coins on the exchange unless you are actively buying to selling them but plenty of people get lazy and just let them sit there.
And if you've got money holed up in Mt. Gox, who's exchange rate is significantly worse than every other exchange, what do you do?
Ask anyone 9 months ago whether or not trusting Mt. Gox was a good idea. They were the largest and most reliable exchange, and now it has become increasingly difficult to get your money out of it. And now the exchange rate on Mt. Gox itself has been effected by their problems...
"And if you've got money holed up in Mt. Gox, who's exchange rate is significantly worse than every other exchange, what do you do?"
I'll tell you what I did, I bought coins and transferred them out of there ASAP. The official line is that their bank will only do 10 outgoing USD wire transfers per day period. Of course limiting outgoing transfers is the same strategy you would want use if you were financially insolvent and wanted to forestall a run on the bank.
Yup, that is the correct strategy, but Mt. Gox's inflated exchange rates punishes you for adopting this strategy. But this is definitely the right way to go.
A friend of mine had money with MF Global, which is a regulated broker. There's some chance it will be coming back within a couple of years. Or not; it's been gone for a while, and so far it seems no one is responsible.
People who banked with Refco, another broker, are even less lucky. The fact Refco's CEO and chairman went to jail isn't helping them.