Yes, in most cases. Each employee can have a traveller profile that holds their name as it appears on their passport, date of birth, document details, contact information, frequent flyer and hotel loyalty numbers, and notes such as aisle seat or a special meal. When that person books, or when the travel desk books for them, those details are pulled into the booking form automatically instead of being typed in again, which also cuts down on spelling mistakes in names.
What happens to the preference after the booking is made depends on the supplier and on the API we are connected to. Loyalty numbers are normally passed through in the booking message and most full service airlines and hotel chains accept them, but some low cost carriers do not take a membership number at all, and loyalty points are often not earned on certain discounted or wholesale rates no matter what you send. Seat and meal choices are usually passed as a request, so the airline can still change them, and some airlines only allow a paid seat selection rather than a free preference.
You also control who can see and edit these profiles. An employee can keep their own, or the travel desk at the corporate client can hold profiles for the whole company. Because passport and date of birth details are sensitive, it is worth keeping editing rights with a small number of people. Profiles can usually be set up in bulk from a staff list your client gives you rather than one person at a time.
Ask your corporate client which details they want stored, then make one test booking with each of their main airlines and hotels to see which preferences actually come back confirmed.