It seems problems arise when dealing with fiat. What about not withdrawing USD, just cryptos?
If I were to use BTC-e only for LTC/NMC into BTC, would I be able to transfer BTC out quickly without issues?
I take a worst case outlook. Like the FBI shuts them down or they simply decide to run off with everyone's coins.
In that case, there is no notice. So no, you wouldn't be able to get your cryptos out either.
Its safer to store locally in your wallet and back your wallet up offsite.