
No, it is not possible to get her registered on the breed register - only her breeder could do that. You could however register her on the Active register so she would be eligible to take part in obedience and agility competition.
As for whether anyone would burgle your house with her in it - who knows? Trained guard dogs have been stolen before now. It's best to assume that her presence will make no difference, and lock up securely as normal.