My experience, and my reflections on it:
In my life, there have been two things which, when first I heard about them, I immediately felt a sense of certainty that they were...well, a part of me. Those two things are Vajrayana Buddhism, as transmitted via Tibetan tradition, and Aikido. In retrospect, I could question that sense of certainty - maybe it was just timing, maybe just a young man's fancy, etc...but in any case I have engaged in both with some persistence and intensity for more than 20 years.
Enlightenment is an experience that is completely beyond conceptual understanding. Anything you can say about it is incomplete, and therefore somewhat 'wrong'. But it is still worthwhile to talk about it, so long as we're careful not to get to attached to the concepts and discussion. Moreover, In a very real way, Enlightenment is omnipresent and instantly available if we simply wake up to it. However, being able to [reside in the experience and dance within the phenomenal world without believing in the dualistic appearance of phenomena], is a very different proposition than having a momentary flash of recognition of the omnipresent ground state. Therefore, there are very few beings who manifest as Buddhas in a way that is recognizable to most of us.
There is no way to "teach" enlightenment. A being recognizes it, or does not. But there are many things a human being can do that increase the likelihood of making a critical discovery, of having an Aha! moment. Engaging in religious rituals can be a powerful method, if one comes to the rituals with correct understanding and correct intention. Engaging in non-religious mindfulness training methods seems to be even more effective; as these methods offer somewhat fewer opportunities to get caught in the trap of being a "true believer".
Taking the classic analogy, let us say that the experience of Enlightenment is the experience of suddenly seeing the moon shining brightly in sky. If Buddhism (or any other discipline) is a finger pointing at the moon, then the study of Buddhism is like studying the anatomy of the hand. Counting the bones, understanding the ligaments and skin, or seeing the spinning chakra in palm - all that is well and good, but at some point, some lucky and perceptive students of the religion look to see where the finger is pointing. Others get stuck on the hand - possibly even to the point where they would go to war with other people whose teachers used a stick to point at the moon, instead of a finger.
So, I don't question whether Aikido teaches enlightenment. To me, that's asking whether it's a stick or a finger. Instead, I ask myself - does Aikido provide a path that supports my awakening at this moment? Does it increase or decrease my emotional confusion? Does it increase or decrease the ossification of my dualistic conceptual framework that obscures my direct perception of ...this very instant of experience?
My honest answer varies from day to day, from moment to moment. And that variance has nothing to do with Aikido; it is entirely due to my own state of mind, my motivation in the moment, and the way I choose to utilize my attention.
That said, when I do answer the question honestly, I find that Aikido is less profound as tool or path to enlightenment than some other things. Chi Gung, Yoga, my meditation practices, the Work of Byron Katie, these tend to be stronger medicine, with fewer side effects - but Aikido is much more fun, so I spend more time and energy on it.
In any case, the path of expanding my experience of enlightenment is a zigzag. Every medicine has side-effects, for which there is another, more subtle remedy is required. Every technique overshoots the mark, and some counterbalance is needed. But right now, I feel my Aikido practice does much more good than harm as I refine my balance and stability, as I release attachments and hangups that hinder my ability to live in the brilliance of Vividly Clear Present Wakefulness Suffused with Joy.