If a booking comes in overnight when my office is closed, can it be ticketed automatically instead of waiting for my staff in the morning?

Yes, in most cases it can, as long as the payment has cleared and the supplier behind that product supports instant confirmation. The usual way this works is that you set rules telling the system which bookings it is allowed to finish on its own, and anything outside those rules sits in a queue for your staff to look at when they come in.

How far this goes depends a lot on the supplier. Most hotel and transfer connections confirm straight away, so an overnight booking is already done by the time you open. Air is more mixed. Low cost carriers normally issue the ticket as part of the booking itself, while fares booked through a consolidator or a global distribution system may need a ticketing step that follows the supplier's own rules and office hours, and some negotiated fares are held back for manual issue on purpose. So the honest answer is that part of your overnight business can be fully automatic and part of it will still wait for a person.

It is also worth keeping some brakes on it. Agencies normally let the system auto issue the simple, low risk bookings and hold back the ones that carry more risk, such as high value tickets, group sizes, infants, special assistance requests, or anything where the name or document details look odd. The system can send you an alert instead of guessing, which is safer than waking up to a ticket you cannot undo.

Ask your supplier or connection provider which of your products can be issued without a person present, then switch auto ticketing on for those first and watch the overnight queue for a few weeks before you widen the rules.