Hi there and welcome to the forums!
Before taking the breeding route and in order to do so more safely, a person should have a very good grasp of the species (this comes with real life experience in budgie ownership) and to do the required research into the subject.
The decision to breed comes with a whole lot of responsibility and commitment, the lives of the breeding pair(s) and the chicks are depending on you and the response you give if/when faced with adversity.
Things like being able to tell if your breeding pair is in good health and top physical condition to go through breeding; when a hen is expecting an egg or if she is showing the first signs of being egg bound; when a chick is having developmental problems, not being fed or showing signs of dehydration;
when there is aggression, abandonment and neglect of the chicks and it's solely up to you to feed and raise the chicks. The ability to detect early on and solve these issues can truly make a difference on the outcome of your breeding journey.
Please read this link: https://talkbudgies.com/budgie-breedi...s-new-old.html
Budgies need to be on a stable and stress free environment in order to breed safely, if all the necessary requirements aren't met and they deem it not safe, then the breeding process can be interrupted.
As for your budgie couple not being tame, this will be a disadvantage because it will make the daily nest checks on the eggs/chicks more troublesome as well as the nest cleaning.
You mentioned the female biting the male. Does she have more of a dominant personality and is it common for your budgies to get into fights?
If there is consistent aggressive behaviour between them and you notice an escalation on the bad behaviour the moment your female went into breeding condition and you added the nest box, then for the safety of your pair and in order to avoid a situation that can end in tragedy for your pair and any future chicks, it's best to remove the nest box and to discourage further breeding behaviour because it's not advisable to breed from budgies who have more of an aggressive/violent temperament: https://talkbudgies.com/budgie-breedi...want-eggs.html