The flash point of fuel is far lower than the flash point of vapourised fuel. Thats why we vapourise fuel when we squirt it into engines. You want to test the cigarette theory, just fill a cup with petrol and drop a ciggie into it from a metre above. If it does catch fire, thats all it will do, catch fire, so its a safe test to perform. It wont ignite, unless you stir the fuel a little just before you drop the smoke.. get some vapour happening.
Enclosing fuel vapour into a canister (or fuel into a dishwasher) and exposing it to flame or electricity is a great way to make a bomb though, I wouldnt dream of trying it.
All a dishwasher does is hit the dishes with high pressure soapy water. It doesnt aim the jets anywhere either, the whole point is to get good coverage on every item in the dishwasher.
If you have a dishwasher that you dont want anymore, it might be useful as a presoak, but I would use dishwashing powder not chemicals, and I would put money on needing to finish the job with a gerni anyway.
I dont see any issues with hurting the dishwasher though, provided you clean and maintain it well. Soap will break down the worst of the oil and grease the same way it does with food.
Probably have not much more effect on the environment in the sewers either once the soap has broken the grease down.. remember the law is speaking of oil in its usual form, not oil which has already been broken down. They use detergents in huge quantities to clean up oil spills..
I honestly dont see much potential benefit over simply spraying on a presoak and hitting it with a gerni personally.. at least you are aiming the gerni (with far superior pressure) exactly where it needs to be aimed.