Organic sugar contains at least 96% of sucrose. The percentage depends on degree of purification. Refined sugar is a highly processed food, so organic origin of the source doesn't effect the product in any significant way.
I try to cook with organic ingredients whenever it is practical. My reasons are not as much health benefits or sustainability as taste. Organic food usually tastes better, if only because it was produced with more care for more demanding customers. Since I cook a lot and my family likes desserts, I researched how sugar is made to decide if it's worth it buying organic sugar. My personal opinion that it's not for my purposes. Here's the gist of my research.
Most sugar consumed in USA is cane sugar. Beet sugar, and particularly organic beet sugar exists in America, but it is rather exotic. The refined sugar passes at least eight stages of purification.
First, the cigar cane juice is rolled out of cane stalks. On the next step, the juice is evaporated and crudely purified from the dirt and fiber with sedimentation process. Next, it is boiled down to syrup, crystallized and separated from the remaining liquid. The resulting raw sugar is already heavily processed food by any standard. It is stored and shipped to the countries there it is consumed. When sugar reaches its destination, it's purified further by filtering, sedimentation, recrystallization and so forth. White refined sugar contains 99.95% sucrose. I doubt any traces of harmful agricultural substances can remain after refinement process.
Organic sugar: demerera sugar contains 97.5%-98% sucrose. Light gold and extra light sugar contain 98% and 99.1% sucrose, respectively. Light brown sugar, brown sugar, and turabindo sugar present different lesser degrees of purification. They have strong characteristic cane smell and contain some water, making it unsuitable for my favorite desserts. Brown sugar obviously retain more raw material and can be more contaminated with pesticide and fertilizer residue, so using organic brown sugar makes more sense. It tastes better than non-organic brown sugar.
Now, cane sugar is not the only sweetener. There are synthetic low calorie sweeteners. There is honey, glucose, maple syrup and so on. There is high-fructose corn syrup used as a sweetener in all processed foods; this one is a poison. The white sugar is, essentially, a drug. Its manufacturing process, its purity requirement are those of pharmacy industry. Sucrose is a disaccharide or glucose and fructose. Both glucose and fructose process in basic energy cycle in every living cell. In those rare people lacking special enzyme needed to break down disaccharide sucrose can cause digestion problems, similar to milk intolerance. Honey contains more monosaccharides, and bioactive components and complex flavor as well. Pure glucose, which is, incidentally, is twice more sweet than sucrose, is available.
See also: kitchen, almond macaroons, chocolate mousse, chocolate truffles, lemon pie.