I said yes.
I don't believe, however, that Aikido drastically and fundamentally alters someone. Something to keep in mind is that Aikido is self-selecting. The people who have an affinity with Aikido, practice it with dedication, and continue to practice for many years, clearly already have some qualities. I would argue that these qualities include a desire for self-improvement, patience, belief to at least some degree in Aikido's principles (harmony, musubi, etc.), inner composure, and an openness to other people. Granted, these are goals. I'm certainly not claiming to possess all of these qualities myself. The point is that we're already looking at a very specialized group of people when we look at Aikidokas.
I would further argue that self-improvement is one of the primary reasons we do Aikido. Surely it's not ONLY for self-defense, physical grace, social connections, or stress relief! Those may be the reasons someone starts, but not why they stay. Speaking for myself, comprehensive (physical, spiritual, mental) self-improvement is the primary reason why I'm still doing Aikido. Do we not strive to harmonize mentally, physically, and spiritually with others and within ourselves? I have trained with very advanced Aikidoka and you can see the difference in their demeanor. It's not mere physical movements that improve over time. I've only been training about a year and a half, but my family, friends, and I have already observed changes. Whether those changes are improvements and make me a "better" person is an impossibly subjective question.
I hesitate to say that Aikido makes someone a better person because that claim seems vague and open to different interpretations. I would claim wholeheartedly, however, that Aikido polishes and improves what is already there. Over years, I think this gradual transformation often has results so that the person seems entirely different. Based on my philosophical beliefs, I would say that self-improvement and "polishing the mirror" does result in a better and more harmonious person.