...Irimi is atemi! ...
In the way we train atemi is extremely important. But more than that it is the potential for atemi that is critical. In irimi we enter into a position where we are in a position of strength and the attacker is in a position of weakness. Our hanmi is directed at the attacker's centre with a low and stable hip posture and we are close enough to be able to deliver a strike with our whole body weight behind it if required. It is this potential for atemi that is critical in our aikido because the attacker will realize his vulnerability and have to cover the weakness, and this will leave an opening for a technique.
I also believe that if you enter to the inside of an attack instead of to the outside you have to atemi or else you will leave yourself open to getting hit yourself. By this I mean that if someone attacks and you enter to his front or inside his attacking arm you are open to an immediate strike from his other arm. We train that you must atemi as part of the irimi to distract the attacker and force him to defend against it, which will force an opening which will allow a technique. We train that irimi is atemi, or the potential for atemi.
I am sure that it is possible to train aikido without actual atemi, but I believe that aikido must include the potential for atemi as a means of upsetting an attack, leading to kuzushi and creating openings for technique. As our Sensei often says, we must always be in a position to deliver atemi if required.