I don't know about amazon selling groceries online, but i do know that some branches of big chain supermarkets (stop and shop and shop rite for example) do have delivery services for actual groceries too. You can place the order online, its (near me anyways) roughly $10 delivery fee and you have to have a minimum of (i believe) $50 before they consider it.
With that said, if the gas expense to drive to your local supermarket is >$10, it would make sense to use a service such as that to get your groceries delivered. I personally live within walking distance of a supermarket, so it wouldn't be sensible for my situation, however I know people on the opposite side of town who do it every other week for either laziness, money saving, busy schedules, or what have you. you do get stuck on whatever prices they have set for your groceries online though...
The service from stop&shop and is called PeaPod (in my area) for what it's worth. If you don't buy processed food, don't start. I've was brought up in a house that ate only processed crap, got fat, bad health, etc.. weened self off of processed food and lost 60 pounds in a year.
just my thoughts :-)