I had the plates fitted early on and have had no issues.
I believe the front bumper has to be removed, but it should be largely a mechanical job, there is no work required on the electrics other than maybe unplugging some connectors, so I would think the risk of major electrical problems is pretty low.
Disconnecting the battery is often standard practice for when working on a car, which may explain the Hybrid Health Check which requires a certain mileage / time period for data to be collected.