Can a secretary or travel desk at my corporate client book trips on behalf of other employees without needing their login?

Yes, in most corporate setups this is possible. The person doing the booking is given their own login with an arranger or booker role, and that role lets them search and book using someone else's traveller profile instead of their own. They pick the employee from a list, the saved passport and preference details fill in automatically, and the booking is stored against that employee rather than against the arranger.

You can usually decide how wide that access goes. One secretary may be limited to a few named directors, a central travel desk may be allowed to book for the whole company, and a department manager may only see their own team. This is worth agreeing with your corporate client before you set it up, because it is really a question about who inside their company is allowed to see other people's travel details, not a technical question.

The approval rules still apply. If the company requires a manager to sign off on a trip, the request goes to that manager even though an arranger made the booking, and the confirmation can be sent to the traveller, the arranger and the finance contact at the same time. Where it gets limited is on the supplier side. Some airlines and negotiated corporate fares need the traveller's own identity or loyalty number at the time of booking, and name corrections afterwards follow the supplier's own rules, so an arranger working from old details can still cause a problem.

Before you offer this, ask your corporate client who should be allowed to book for whom, and check that the traveller profiles are complete and current so the arranger is not booking on guesswork.