I'm going to attempt to talk from personal experience about a very subjective topic in a meaningful way to the conversation.
I see the spirituality of O'Sensei (from the little I am familiar with) as finding concrete form in the ethics of Aikido. Whether you believe he achieved enlightenment, or whether one can achieve enlightenment through Aikido; O'Sensei's personal beliefs and philosophy formed the ethical basis of his Aikido and it is one of his most enduring legacies to the art. Rather than trying to speak in terms of "spirituality", which is a matter of semantics in many respects, I think speaking "ethically" is far more constructive in this particular instance.
As a Christian I do not adhere to Buddhist, Daoist or Shinto beliefs or doctrines, however I can agree on Aikido's ethical framework. There are many scriptures in the Bible that support the ethics of Aikido. O'Sensei may have arrived at those ethics through different means than myself, yet nevertheless they converge through the application of Aikido as budo.
As a Christian I am concerned with peace, non-resistance and love. I strive to embody these ideals and the Biblical teachings that provide the ethical framework for these abstract realities. Aikido/Aikibudo is a vehicle through which I can learn to develop meaningful expression of these ethical values.
In such a way I could consider my practice of budo as a form of my "spirituality", but my spirituality is not strictly defined by Aikido or any other kind of budo. I am first and foremost a disciple of Jesus Christ. I could express my spirituality using the same vernacular as Graham Christian, but it would carry very different connotations because its source is very different again.