On a sidenote, I'm stifling a giggle.
Noiseless shouts, thanks to illusion. Mindboggling!
I was wondering the very same thing! I didn't have a chance to test that, though.
I posted a thread very similar to this a little earlier today

http://www.gamesas.com/topic/1329490-fire-breath-frost-breath-and-destruction-magic/
Basically the elemental shouts do pathetically little damage, even with everything you can do to boost them. The question of whether or not they are boosted by the Destruction perks hasn't been answered, but I would hazard a guess and say the shouts ARE improved by Destruction perks.
EDIT:
According to the UESP wiki, which looks at the game files to extract the effects, the damage of Frost Breath is grouped under "Frost Damage", just like the Frost Destruction Spells AND the Frost Damage Enchant you can put on your weapons. I know that having the Augmented Freeze perk will stack with the Enchanting perk for enhanced frost damage and give you a massively damaging enchant, so by that logic the breath shouts should be improved too.
If we're going by that, the strongest possible Fire Breath you can get is:
18 * 1.5 * 1.25 = 33.75 dam / sec for 5 secs.
That's actually far more reasonable damage than what it seemed like before, which was just slightly stronger than the basic Flames spell! Also I didn't factor in the possible Aspect of Terror boost because I wasn't sure if it would apply.
I was active on your thread, but it didn't get any hard numbers except for Frost Breath (from UESP), which I wasn't even sure was accurate (I've done a lot more damage than what was posted on it, I'm sure). I also wanted to create this thread for clarification's sake; I'm not just asking about Destruction, but all shouts and magics being affected both ways. Credit to you, most obviously, as you intrigued upon me such an interesting curiosity

Where did you get those numbers, though?
I don't think the mundane magical skills will have an effect on the shouts, you get a perk through a quest that enhances the fire shout damage so this again suggests to me that the shouts are treated as seperate from the other magical schools.
Not true, friend; shouts are treated just like magic. They can be absorbed, resisted, warded, etc. I'm just wondering how far that etc. goes; does Fire Breath cause Fear, is Storm Call a resisted effected, all that.