Yes, in most cases you can show prices in your local currency even when the supplier quotes in a different one, though how smoothly it works depends on the supplier and on your plan.
The way it normally works is that the software receives the fare or room rate in whatever currency the supplier sends, then converts it for display using a rate you control. You can usually choose between a rate you set yourself and update when you want, or a daily rate the system picks up automatically. Your markup and any rounding you prefer are applied on top, so the customer sees one clean figure in the currency they are used to. You can also set different display currencies for different websites or different groups of customers if you sell in more than one market.
There are limits worth knowing. Some suppliers will only settle with you in their own currency, so your cost stays in that currency even though your customer pays in yours, and a movement in the rate between booking and settlement can eat into your margin. Your payment provider may also only accept a certain set of currencies, which can decide what you are able to charge in. Refunds and cancellations are usually returned in the supplier currency, so a rate change can leave a small difference when you pass the refund back. Many agencies allow a little buffer in their markup to cover this.
Before you decide, check which currencies your suppliers settle in and which ones your payment provider accepts, then tell us the display currency and the rate source you would like configured.