Yes, it usually can. The software keeps a profile for each customer, so once you have sold a trip to someone their name as it appears on the document, date of birth, nationality, passport number and expiry date, and their contact details can be stored against that profile and pulled back the next time they travel.
In practice your staff start a new booking, search the customer by name or phone number, pick the right profile, and the passenger fields fill in on their own. You can keep more than one traveller under a single customer, which helps with a family that always travels together or a company whose staff you book for often. Everything stays editable before you send the booking, and that matters, because passports expire and an airline will reject a document that is out of date or spelled differently to the ticket.
There are honest limits. Which fields are saved depends on your plan and on how your portal has been set up, and some suppliers insist that document details are entered at the time of booking rather than accepting a stored value, so a profile saves typing without removing the check. Holding passenger documents also brings you under the data protection rules of your own country, so keep only what you need for booking and decide which staff are allowed to see it. Access can be limited by the role you give each login.
The next thing to check is which passenger fields your booking form saves today, and what a normal staff login can see when it opens a saved profile, so you can set permissions the way you want before your customer list grows.