Yes, a white label travel portal can be found on Google, but it will not happen by itself and it takes time, so please do not expect search traffic in the first weeks after launch.
The pages that search engines usually pick up are your home page, your content pages, any city or destination pages you create and anything you write yourself, such as travel guides or offers. The live search results pages are different. They are built fresh every time a customer types in a date and a destination, so search engines often do not store them. This is normal for every booking website, not a fault in your portal. It also means your own written content is what brings in strangers, while the booking engine is what turns them into customers once they arrive.
How much you can do depends on your plan and how the portal is set up. Some plans let you edit page titles, page descriptions and add your own pages, and let you connect your portal to Google Search Console and an analytics account so you can see what people search for. Others give a fixed set of pages. Supplier terms can also limit how much of a hotel description you are allowed to republish as your own text. Using your own domain from day one matters too, because moving a site later means losing some of what you built up.
Before you launch, ask us which pages on your portal you can edit and index, get Search Console connected early, and plan on paid ads, social media and your existing customer list to bring in bookings while your search traffic slowly grows.