Yes, breakfast cereals are often very refined simple carbs.
The theory behind iDave as I understand it* is minimising insulin production. Insulin makes your cells take up blood sugar and makes you lay down fat (as far as I can gather).
So if you eat simple carbs they get digested very quickly and your blood sugar goes up, so your pancreas needs to dump loads of insulin in your blood to stop your brain dying (or something). This clears out your blood of sugar quickly and you're back to square one in no time. (low blood sugar is one of the things that makes you feel hungry).
The exception to this is when you are riding and your cells need lots of energy transported to them, and just after exercise when their stores are depleted (your cells can use up the energy faster than your guts/blood can deliver it)
iDave cuts out things that produce insulin - for the purposes of minimising fat creation. However it also means that what you do eat gives you energy for longer.
It's also an incremental thing. So if you cut down somewhat on insulinotropic stuff you'll get some benefit - if you really cut down a lot you'll get more of an effect. I'm finding I am less hungry on iDave and want to snack much less because I am eating a lot of 'filling' foods. And still losing weight. You don't have to hold back, unlike calorie counting - you can fill your face on whatever's on the list. I miss sweet stuff a lot though, but I don't go hungry.
* I could be talking rubbish here, someone please put me straight.