Nothing in the Bible gives me cause to view my Aikido training as a spiritual pursuit. My spirituality is bound up in a relationship with a person (Jesus Christ), not a physical activity. (This isn't to say that my spiritual life doesn't manifest itself in a physical, tangible way -- it does. However, there are clearer, more constructive ways that this takes place than through twisting the arm of my partner in Aikido training.) In my thinking, then, Aikido and spirituality have little to do with each other. And because I believe this to be true, I don't introduce any kind of spiritual or religious teaching into the Aikido I teach my students. From my perspective as a Christian urging my students to view Aikido as a spiritual pursuit would be tantamount to urging a blind person to watch a movie.
I think Aikido is spiritual in the same way washing a car can be spiritual: it's what you put into it that nurtures the soul; not the actions themselves. Personally, I'm not big on people urging one another on how to act spiritually. One of the reasons I really like my dojo, a religious center in fact, is that this is always so well respected. That said, I can also see why folks would apply a Martial Art to their spirituality (or vice versa, more likely).