Well, sanitizers are industrially-produced chemicals, so it's hard to conceive of an "organic" sanitizer. The "organic" label generally refers to how produce and livestock are grown, and sanitizing solution is not something that grows on a farm.
I made a soup once that I thought was pretty good. I was stoked because I had inadvertantly made it vegan. I had one of my servers taste it and he commented that it tased like it had chicken broth in it. I assured him it did not and ran down the list of ingredients. Another server was listening and as she left the room reminded me that Worcestershire has anchovies in it. From vegan to not even vegetarian in 2 tbsp.
What you have is a beer made from organic ingredients.
That is a really good question. https://cdn.homebrewtalk.com/images/smilies/occasion14.gif
Of course beer is no longer organic once it comes into contact with sanitizer. By legal definition in the US organic food or beer must only contain organically grown ingredients, water, salt, and a few select naturally occurring minerals that have been reviewed for inclusion by the USDA. Chemicals like Star San are definitely not on the allowed list.
When organic beer is brewed commercially sanitizers are only allowed if the procedure includes a final rinse of sanitized equipment with sterile water or steam to remove all sanitizer residues. Homebrewers can also accomplish this by having some pre-boiled water on hand for a final rinse.