Yes, you can. Travel agency software is usually built for both sides of the business, so as well as the website your customers use, your staff get a back office where they can search, quote and book for someone at the counter or on the phone. The booking lands in the same system either way, so your sales reports cover the whole shop and not just the online part.
On payment, a counter booking is normally recorded by choosing how the money came in, such as cash, a card machine in your office, or a bank transfer, and then marking it paid or part paid with a balance still due. That gives your accounts team something to reconcile against. Whether you can charge a card directly through the system at the counter depends on the payment gateway you are set up with, so it is worth confirming rather than assuming.
Two things often help walk in trade. Staff bookings can usually be taken against your own agency balance instead of the customer's card, which suits someone paying cash later in the week. Many setups also let you add a booking by hand for something you arranged outside the system, so your figures stay complete. What you can actually sell at the counter still depends on the suppliers connected to your account.
Before you go live, ask for a walk through of the back office booking screen with the staff who sit at the counter, and check which payment methods your plan lets them record.