an interesting theory. . . id say it IS possible, but not very common
it would do the same as a starter on a full petrol motor but it would be starting the electric motor instead, with it being a push button starter it may well be easier, youd probably set the unit to voltage sense to stop 'cranking' since obviously you arent cranking over a starter motor, and nor would you have a tach signal to read succesful start up. . .
this sort of thing would only really work for summer time though since the electric motors can spin the A/C compressor, but they cant heat up coolant for the heater to work properly without the petrol motor spinning and generating heat, but I guess eventually either way the petrol is going to fire up since I assume the batteries wont sustain full systems all that long