It can be done but there are some, well 'buts'
You need petrol to start until the engine is warm enough to evaporate the LPG, you'll have noticed the evaporator is heated by the engine coolant.
Most systems use the enigine revs to determine that the engine is running before opening the gas valve, otherwise the gas would fill your underbonnet area and go BANG
The systems that can runn entirely on LPG tend to be the latest, fully automated, multi point systems and these often piggy-back from your EFi anyway, but they cost the earth and have lots of electronics.
So you could probably do it with a sort of 'start' button, like on plant machinery where they hold the glow-plugs on for a while but in your case keeping the gas-valve open untill the system kicked in. I'd keep the button well covered though, which would also make it hard to nick!
