For approx. a month, I attended classes at a classical Japenese Jujutsu school before choosing aikido instead(partly because of the difference in attitude at the two dojos, and mostly for monetary reasons). During a given technique, nage would insert various atemi, not neccessarily because they needed to distract Uke, but because uke was open. And that is what I think is the essence of any given technique- moving into a place where relative to you, uke is open either for an attack via an atemi or a technique. If the technique fails, and uke slips out, you are in a position where uke cannot attack and you can. If you do not use the atemi at all, and don't even aknowlege openings for atemi during practice, you are missing out on a VERY important part of aikido. Also, much of hte positioning that is desirable for nage cannot be facilitated without at least the threat of atemi. Why sweep your foot back to protect yourself when you know that your opponent isn't going to strike you?
One thing that isn't evident in the dojo, however, is that atemi are not always condusive to completing a technique. Often times, if your atemi connects it may distract uke, but it certainly doesn't make the technique any easier, as uke is more likely to curl inwards. If you can find someone who is willing to have you punch them somewhere at a random moment, you'll note that they pull back and protect themselves when it. Also, non connecting atemi, such as hand in the face only work really well against trained fighters. Most people simply don't have the reflexes to move away from your hand in the same way that someone in the dojo does.
Another problem is that atemi can mean giving your opponent your hand.
Here's an example:
shoot a tegatana to uke's face in ai hanmi and get them to parry it
with their leading hand leading directly to ikkyo.
Why would they block it when they could simply do ikkyo to you instead of blocking? Or if they practiced some other martial art, bat your hand down, make it unable to block, and strike you?
As someone else in this thread pointed out, though, atemi can be more harmonious than aikido in some cases. Why attempt a technique, be it osae or nage waza, when you could just give your opponent a single solid kick to the groin? Done at high speed, with adrenaline, many aikido techniques have a potental to break bones(esp. nage waza).
These are just my thoughts on the subject. I haven't been doing aikido for terribly long, but I just figured I'd add my 2 common cents. I didn't vote in the poll. My answer is 100% and 0%. It all depends on the situation. I think bruce lee had the right idea- do what you can, when you should. If you cannot do a technique, then do one that you can instead if it'll work as well.