Maybe the problem is semantics. It's hard to argue with any of the logic presented so far. It is simply a matter of perspective: How much of making an automobile run is gasoline? Actually, probably only a small percentage, but without it you ain't gonna go far.
Atemi is what sets up technique, distance and timing, but if you are unaware of that fact, and doing Aikido in a set pattern because that's how it is taught, how will you ever learn proper technique? Conversely, if you are aware of the role of atemi, and use it properly, how big a part of your Aikido is it? It is important to breathe and move, but how much do you really think about it?
So maybe for many respondants atemi isn't a big part of Aikido on a conscious level, but that doesn't mean it isn't there?