Yes, you can see the total price through the API before your customer books. When you search for flights, the API returns pricing information that includes the base fare, taxes, fees and any other charges that will apply to that booking. This means you know the complete cost upfront and can show your customer exactly what they will pay before they click to purchase.
The price you see in the search results is what your customer will pay at checkout, so there are no surprises after they commit. Some airlines and routes may have different fee structures, and those differences will show up in the total price the API returns. You can compare prices across different flights and airlines by looking at these totals side by side.
Keep in mind that prices can change between the moment you search and the moment your customer actually books, since airfares update constantly throughout the day. The API shows you the current price at that moment, but if your customer waits before completing their purchase, the price could go up or down. If price changes matter to your business model, you may want to check how long a price hold lasts with each supplier before building that into your workflow.