No.
>should I be spending the same money and energy on eating less sugar and more of any kind of produce?
Yes.
It is no surprise you feel torn. Tons of money is invested into the marketing of "organic" produce when it has, in-fact, ZERO positive gain over conventional produce. The FUD being forced down everyone's throat by the "organic" industry is designed to make you feel exactly like that. When you introduce doubt, you create a path to convince folks into spending money on your product.
But don't take my or anyone else's word for it. If you can muster the time, spend an hour or so perusing Wikipedia, reading articles and collecting sources and you'll find in relatively short time the "organic" thing is solely a money grab. With "organic" food, you are getting the same exact thing grown by conventional methods but at a higher price.
Groups such as the one mentioned in this article don't want you to perform your own research, they just want you to believe what they have on their web site. It's bogus.