As the RNS310 is relatively new I would be highly surprised if you can run RNS510 Firmware on it. For a start there is no HDD on the 310 which is updated with the firmware and they are made by 2 diff companies (RNS310 Blaupunkt and RNS510 VDO Continental)
The 310 will plug and play but it will all just work from the unit. For Nav Instructions on Highline & Steering Controls etc it will need coding with VCDS.
You can get a new Can Gateway for around £85 off fleabay. Or about £130ish from a Dealer. This will be the only way to stop Battery Drain until more of these units become available and people start acquiring the Firmware to modify.
HTH
Carl