Can you leave your cockatiel alone for a week?

Its not really a good idea. Even if you leave enough feed and water you never know what will happen. The seed could get knocked down and then its water dumped on it rendering it inedible. Even if all went well the cage will be filthy and that is simply not a healthy situation. Your bird might sort out how to open the cage doors, yes it has happened, then your bird has free reign. Who will cover the cage at night? What if they get sick and need a vet?

Birds are like small children; you never know what will pop into their heads to do next. You wouldn't leave a small child home alone for a week with lots of food and liquid available would you?

Get a friend to come in at least once a day to look after your fid, board them at a pet store or vet, contact a dog walking/house sitting service to see if they will come and see your friend.

Do not leave them alone for an extended time.