Yes, a chatbot can handle a good share of the questions that come in after your office closes, as long as you are realistic about which questions those are. The ones it does well are the repeat questions your staff are tired of answering, things like what is included in a package, how much baggage the fare allows, when the balance is due, what documents the customer needs, and what the cancellation terms say. If it is connected to your booking system it can also look up a booking reference the customer gives it and tell them their flight timing or confirmation status, so they go to bed with an answer instead of an unanswered message.
The important thing to understand is that a chatbot only knows what you have given it. If your cancellation policy or visa guidance is not written down anywhere, the bot has nothing to draw on, and you do not want it filling the gap with a guess that your customer later holds you to. So the quality of the answers depends almost entirely on the quality of the material you feed it, and that part is your work, not the software's.
There are also conversations that should never end with the bot. Anything that changes a booking, moves a date, promises a refund or takes a payment should be passed to a person, with the chat history attached so your staff are not starting cold in the morning. Whether the bot can read live booking or fare data at all depends on your suppliers, what their APIs allow and which plan you are on, so that is worth confirming rather than assuming.
Before you switch anything on, write down the handover rule, meaning exactly which questions the bot answers and at what point it says a colleague will come back to you, and then read the overnight chats yourself for the first few weeks to see where it is getting it wrong.