Will I be able to buy and sell cryptocurrency and keep a fiat balance on the exchange?

Yes.

The PlutusDEX is used for buying and selling Ethereum, and of course Pluton. On the PlutusDEX, your fiat balance is held until the purchase is completed, and then the balance is transferred to the user who provided the cryptocurrency.

You can find a detailed guide on how to utilise the PlutusDEX here