Can my travel agency software send booking updates to my customers by text message or WhatsApp?

Yes, in most cases it can, although the messages themselves go out through a separate messaging provider rather than from the travel software on its own. The software knows when something has happened to a booking, so it can pass that moment on to the messaging service and have a short note delivered to the customer's phone.

The events that usually make sense are the ones your customers already ask about. A confirmation once the booking is held, a note when the ticket or voucher is issued, a receipt when a payment goes through, a warning if the airline moves the flight, and a confirmation if the booking is cancelled. These are the same moments that trigger your emails, so nothing new has to be invented.

There are limits worth knowing before you promise it. WhatsApp business messaging needs an approved sender account, and the wording of anything you send first has to be approved in advance as a template, so you cannot write freely outside the window when a customer has replied to you. Text messages need a registered sender name in many countries, and some countries have their own rules about that. The cost of each message sits with the messaging provider and varies by country, and you also need the customer's agreement to be contacted this way.

If this matters to you, check whether messaging is included in your current plan or needs a separate account, decide which few booking events really deserve a message, and start the sender approval early, because that part often takes longer than the setup itself.