Glucose acts as willpower fuel. As willpower levels drop, so do glucose levels. Willpower can be restored by raising your blood sugar.

How strong do they claim this effect is? Does it work for higher-than-normal BG (to raise willpower) or only lower-than-normal (to lower it)?

I'm a type-1 diabetic and have been in both situations a lot. More generally, type 2 diabetes is so widespread today that there's a huge amount of (unreliable) data about diabetics. If this claim is true, I'd expect it to show up in metabolism research.