You could do anything you like without permission (I'm guessing) as long as you're not making any money or passing it off as a legitimate product, that includes any advertising, free or otherwise.
... and still could get slapped with a cease-and-desist letter. You don't have to be making money, to be violating someone's copyrights, nor (especially) Trademarks.
With that said, if it's not about the money ... a pitch to be allowed to write and distribute, without charge (but perhaps accepting donations), a clearly-marked-as-UNofficial PnP adaptation, might have a better chance of success. Maybe.
At which point, you could simply go with a pure PDF distribution model, and contact any of the number of online shops that will (at least on occasion) distribute free products. For two examples: http://www.rpgnow.com/ and http://rpg.drivethrustuff.com/.