Do Unitarian Universalist churches acknowledge the possibility that the Quran may be the inspired Word of God?

Your question intrigued me and so I checked out the information in that Wiki article you partially quoted from. I found this reference to Islam:

The beliefs of individual Unitarian Universalists range widely; they can include, but are not limited to: humanism, Judaism, Christianity, Islam, Hinduism, Sikhism, Buddhism, Taoism, syncretism, Omnism, Neopaganism, atheism, agnosticism, pantheism, panentheism, pandeism, deism, and teachings of the Baháʼí Faith.

Mention of Islam was made in this article:

Unitarian Universalist congregations have become religious homes to many people who have a personal relationship with Islam. Whether raised Muslim, married to a Muslim person, or simply inspired by Muslim teachings, a growing number of Unitarian Universalists weave strands of Islam into their faith today... Our worship services, which draw from many sources, may include a reading from Islam’s sacred traditions, a passage by a contemporary Muslim author, or a poem by a Sufi mystic like Rumi or Hafiz. https://www.uua.org/beliefs/what-we-believe/beliefs/islam

Unitarian Universalists do not refer to the sacred texts of other religions as being inspired by God. Furthermore, it seems that the Bible and other sacred writings are never taken as the only word, or the final word. https://www.uua.org/beliefs/what-we-believe/sacred-texts

This book, ‘Children of the Same God - The Historical Relationship Between Unitarianism, Judaism, and Islam’ by Susan J. Ritchie, published by Skinner House Books, says that ground-breaking research shows that Unitarianism was inherently multi-faith from its beginnings, with clear affinities for Judaism and Islam. The book re-examines Unitarian history in the light of its interfaith context.

It’s rather difficult to pin down how Unitarian Universalists view God. Yes, they believe in “a higher power” or authority, but is this the same God of the Bible?

>What Do We Believe about God? Unitarian Universalists have many ways of naming what is sacred. Some believe in a God; some don’t believe in a God. Some believe in a sacred force at work in the world, and call it “love,” “mystery,” “source of all” or “spirit of life.” We are thousands of individuals of all ages, each influenced by our cultures and life experiences to understand “the ground of our being” in our own way. Unitarian Universalists are agnostic, theist, atheist, and everything in between... We join together not because we have a shared concept of the divine. Rather we gather knowing that life is richer in community than when we go it alone. We gather to know and be known, to comfort and be comforted, to celebrate the mystery that binds us, each to all. https://www.uua.org/beliefs/what-we-believe/higher-power

I found an official Unitarian Universalist article promoting a publication “What we Believe”. It does not say that they accept the Qur’an as being “the inspired word of God”. Neither do they say they accept the Bible as being “the inspired word of God”. I will post the introduction and leave the link for anyone who wants to find out what six other Unitarian Universalists think about the Bible and other “sacred writings”:

What we believe: Introduction by Rev. Tom Goldsmith, Editor - First Unitarian Church Salt Lake City: UU [Unitarian Universalist] Views of the Bible offers a glimpse into six spiritual journeys. One originates with an impassioned fundamentalist embrace of the Bible while others begin with the Bible as suspect. All of the journeys are refreshingly thoughtful, a bit provocative, and even humorous. The pamphlet offers no critical analysis of the Bible, interpretation of the historical Jesus, or promotion of the Darwinian theory of evolution over and against creation theory. Instead, it gives the reader a very frank approach to a text that is often misquoted, misinterpreted, and mistreated.

The six UU contributors describe their particular relationships to the Bible, and address more generally the relevancy of scripture to religious liberals. All contributors agree that the Bible is riddled with historical errors but nonetheless can serve as an important repository of human truth. Does the Bible have any significance in their lives at all? Each voice in this pamphlet renders a unique and stirring account of the Bible's continued vitality for religious liberals in the twenty-first century. https://www.uua.org/beliefs/what-we-believe/sacred-texts/bible

I can only conclude that Unitarian Universalists accept many "sacred writings" as containing wisdom, perhaps even divine wisdom, but nothing to suggest they believe the Qur'an is "the inspired word of God".