Batteries just seems like such an odd choice here when there are existing solutions in the market.
Batteries keep working after the burglar's been in the meter cupboard and shut the power off. Whether that's true of the whole Nest security system the article isn't clear. But in the UK, where most houses built over the past thirty plus years have externally accessible and unsecured electricity meter cabinets (with a master switch), any effective alarm needs full battery back up for a considerable time.