They do convert all fiat money that is deposited into their accounts into dollars, but I don't know where those dollars are held. I don't understand why they do this though, because they do issue EUR and JPY IOUs and that seems to entail unnecessary exchange rate risk.
Since they
do convert everything to USD, they are
not at exchange rate risk.
If I deposit 100€ when EURUSD is 1.3, I get 130$ in the Bitstamp account, and they likely internally held it in USD.
Then if EURUSD drops to 1.2 and I withdraw, I get 108€, thanks to the new exchange rate. But they didn't lose anything, if they really converted the currencies, rather than only "displaying" it.