Hi C! Yes mineralized veggies and fruits will have a longer shelf life, this is well documented and calcium is often used as a food preservative in the junk food industry!
Rabbits and higher life forms like Raccoons and humans actually will prefer high brix foods and shun your neighbors low quality produce for yours!
A fence and a shot gun may be necessary to keep away unwanted guests in your garden, four legged or two! A dog can help also!