Here is DomeGaia's somewhat official statement on aircrete domes and building codes. I like that it is much more positive than my personal view.
First, check with the local building regulations. Usually you can build unpermitted structures up to a certain size. In Hawaii you can build unpermitted up to 200 sqft on residential land, and 600 sqft on ag land.
You may find that it's not a big deal to get your Aircrete structure permitted. People build unconventional permitted structures all the time. Typically a stamp from an engineer licensed in your area is required to release the county of any liability. Here in Hawaii the authorities only interfere if there is a complaint. You could go to your neighbors and show them your plans to build without a permit. If they are like most people, they'll want you to build one for them too!
Unconventional structures, such as Aircrete domes, typically require a stamp of approval from an engineer or architect licensed in your county. This releases the county from liability. You'll have to check with your local building department for specifics. Your building department may even recommend an engineer or architect to you.