That could happen. However, it seems the spread has reduced a bit.
Instead of around $100 in difference, it's now around $80. It doesn't mean anything unless the premium will drop further in the coming days. If that would happen without public notice, then the chances are high that certain entities know something that others don't -- insider trading. MtGox eventually didn't allow people to cash out anything -- no coins, no funds. As long as Bitfinex allows people to cash out digital currencies, people will not panic.
The clients and an exchange itself will not panic as long as there will be a people sending bitcoins there with a hope of easy money on arbitrage. From an exchange stand point of view its not a big deal if they are going to give someone else bitcoins.