They should be able to unless malicious intent is involved or their servers get overloaded but eventually everyone should be able to get their bitcoins out as long as security is in place.

Even if everyone withdrew their Bitcoins from Mt. Gox into private wallets, it shouldn't cause Mt. Gox to go bankrupt as they are not a bank but an exchange and take a commission cut on each transaction.

The only way that this would be a problem is if someone sets up an exchange but then gives people "fake" bitcoins to people that leave their bitcoins with the exchange. They would have real bitcoins around of course if people withdraw them but it would turn into a juggling act and eventually fail if too many people withdraw their bitcoins.

I don't want to say it's farfetched but it's probably better to store your bitcoins yourself in your own wallets rather than leaving a significant amount in the control of someone else.