Not always, and it is worth understanding why before you promise anything to a customer. Hotel rates and room availability come straight from the suppliers, and they can change at any moment because other agents and websites all over the world are selling the same rooms. A room that was available and priced one way when your customer searched can be sold out, or repriced by the hotel, a few minutes later. No booking system can freeze a supplier's rate just because someone is looking at it.
What a good hotel booking setup does is check the room again with the supplier just before payment is taken. If the rate and the room are still exactly as shown, the booking goes ahead quietly and your customer never notices anything. If the supplier comes back with a different price or says the room has gone, your customer is shown the change and asked to agree before any money moves. That way you are never left having charged one amount and owing another to the supplier.
How often this happens depends entirely on the supplier and the destination. Quiet dates and ordinary city hotels rarely move. Peak season, event weekends, last minute bookings and very popular resorts move far more often, and some suppliers refresh their rates much more aggressively than others. It also depends on which suppliers are switched on for your account, so the experience is not the same for every agency.
It is worth telling your staff to treat the search price as an indication until the booking is confirmed, and to check with us that the recheck step before payment is active on your portal.