Yes, a white label travel portal is built to work on a mobile phone as well as on a desktop computer. The search boxes, the results pages and the checkout adjust themselves to the size of the screen, so a customer looking for a hotel on their phone sees the same rates and goes through the same booking steps as someone sitting at a laptop. Most travel businesses now see a large share of their visitors arrive from phones, so this is treated as a normal requirement and not an extra.
There are a few honest limits. Your portal controls how its own pages look, but some parts of the journey are handed over to other companies, for example a card payment page belonging to your payment gateway or an airline page in a redirect flow, and those pages look the way that company designed them. Hotel photos and descriptions come from the supplier as well, so on a small screen a very long description may simply need more scrolling. Vouchers and tickets are usually PDF files, which open fine on a phone but are easier to read on a bigger screen.
It is also worth separating two different things. A website that works well on a phone is not the same as a mobile app that customers download from an app store. An app is a separate piece of work and whether it is available to you depends on your plan, so please ask us before you promise one to your customers. The staff side of the system, where bookings and reports live, can be opened on a phone for a quick check, but everyday work there is more comfortable on a computer.
The best test is your own hand, so while your portal is still in its trial stage, please run a search and a complete test booking on your own phone, and tell us about anything that feels cramped or hard to tap so it can be sorted out before you go live.