Yes. The white label travel portal is built to adjust itself to the size of the screen it is opened on, so the same site works on a desktop computer, a tablet and a phone without you needing a separate mobile version. Search boxes, results and the booking form all reflow so a customer can go from searching to paying on a phone in one sitting.
There are a few places where the experience depends on someone other than us. When a customer pays, they are often handed over to the payment gateway's own page, and when they pick seats or add bags, some of that content comes from the airline or hotel supplier. Those screens are controlled by the supplier or the bank, so how neat they look on a small phone is their design, not ours. Most are fine these days, but it is worth knowing where the line sits.
It is also worth being clear that a mobile friendly website is not the same thing as a phone app you download from an app store. The portal is a website, so it opens in the phone's browser. If you want a proper app with your own icon on the home screen, that is a separate piece of work and whether it is available to you depends on the plan you are on, so ask before you promise it to anyone.
The best check is a practical one, so before you go live open your own portal on your phone and your staff's phones, run a real search, and go all the way to the payment step to see how it feels in your hands.