Just a few points . . . .
I removed my air dam months ago and have never experienced hood flutter. For what it's worth, I did replace it a few weeks after removal with a (much smaller) skid plate from Elevated Offroad. I wasn't tracking gas mileage before, so I don't know whether I had a drop. That's not a warranty issue though.
Common sense dictates that the air dam provides some barrier to liquid and debris coming into your engine compartment. The pics Daggo posted would of course be beyond its capacity--that's like trying to stop a waterfall with a bucket. But for basic splishes and splashes, sure, it blocks a little. Regardless, the engine compartment should always be on your checklist for post-wheeling cleaning. I think earlier threads established that hosing off the engine is no problem so long as you just don't directly spray the electronics.
Jimbox's example is pretty text book. The warranty won't cover the modded part (the removed air dam) or damage caused by the modded part (the removed air dam), so that all makes perfect sense. However, it's also worth noting that the warranty wouldn't have covered the jeeper in the story anyway--he was offroad and "abusing" his Jeep. Trail damage ain't covered.
Finally, in my view, a JK looks a hell of a lot better without an air dam!