Better fuel economy? I don't understand... how is the AP going to give you better fuel economy?
If you're referring to the "Fuel Economy" map, it's useless. You get the same effect by keeping a light right foot. In fact, I have a fundamental problem with that map altogether... at least by keeping a light front foot, you can stay out of boost but still have that oomph when you need it. With the Fuel Economy map you'll just get caught with your pants down.
To answer your question, the AP stores your CURRENT map when it marries, so technically it will be your OS tune after it's unmarried.