In Australia can someone has a an interest in property by adverse possession bequeath the property to an heir? If so, will that claim be able to defeat the interst of an heir of the legal owner?
Adverse possession is not a property interest
You seem to have the idea of adverse possession backwards. If you adversely possess my property then I have a cause of action against you - you don't have a cause against me. You can become the owner if I fail to take such action within the required time. If that happens you can apply to become the owner - my only way of preventing this is to prove that the statute of limitations has not expired.
(2) Subject to subsection (3), where a cause of action accrues to recover land from a person in adverse possession of the land, and the land is afterwards in the adverse possession of a second person, whether the second person claims through the first person or not, the cause of action to recover the land from the second person accrues on the date on which the cause of action to recover the land from the first person first accrues to the plaintiff or to a person through whom the plaintiff claims.
So while you cannot "inherrit" an interest, if you maintain the adverse possession started by someone else, the time runs from the initial adverse possession.