An fi bike will just cut out when there is no fuel entering the pump, as the pressurised side of the system is full of fuel, the bike will start straight away once refilled.
I'm sure there are lots of opinion of how to store a bike long term - how long are you anticipating?
I'd be tempted to leave full with stabiluser as long as it will keep the fuel good for that length of time.
If the tank is drained, take measures to prevent rust forming in the tank.