I am fairly new to Aikido just joining an Aikikai dojo a few months ago, but do have quite a few years other Japanese arts, so I would like to think I speak with a little experience.
I believe atemi is required when it will aid in achieving the desired effect. That aid may be either supplementing the physical dynamic of the particular technique, or aiding a technique by shortening the time needed to complete it.
The example you gave of the woman seems to demonstrate the the atemi she employed actually detracted from the technique, since it added to time to the completion of the immobilization (or projection), and added no other value (such as affecting kuzushi).
Should you do atemi if it will not hinder a technique? Why do it if it is not necessary, and the technique will carry itself? Should you do it if you expect resistance, and need a distraction? By all means!
There my be some other considerations in aiding the technique. For example, it may not be needed to supplement a technique in itself, but it may be needed to supplement a situation such as facing multiple opponents. The atemi used in such a scenario may hopefully keep opponent #1 pre-occupied with himself while you take care of opponent #2.
I believe you are very much like me. I tend to want general rules or guidelines when it comes to certain aspects of martial arts. I like the idea of not having to put a lot of thought into what I'm doing, and just reacting to a certain attack (or other stimulus if you will). I believe atemi is one aspect of the art where such thinking is not always so easily accommodated.
Well that my 2 cents anyway.