Utah will override any state constitutional provisions if other states start allowing it and possibly would do so before to be the first state to legalize it.
That would throw it into federal court, depending on who had the standing to challenge it, because the Utah Constitution says that the prohibition against polygamy cannot be changed without permission of the United States.
The wild card in this would be if a federal court strikes down a polygamy or bigamy law elsewhere on the basis of Lawrence v. Texas, 539 U.S. 558 (2003). Kody Brown and his Sister Wives have filed suit claiming that Utah's bigamy law should be struck down. I haven't read the pleadings, but press reports are it's primarily on Lawrence grounds. Utah's bigamy law (Utah Crim. Code § 76-7-101) doesn't just apply to marriage; it applies to a married person purporting to marry another person or cohabiting with another person. Utah's attorney general says that Lawrence doesn't apply, because Lawrence's privacy (sex between homosexuals) is privacy between two people; polygamy involves children, child custody, alimony, and things that aren't part of the penumbra of privacy. From the viewpoint of legal analysis, a Lawrence-based polygamy challenge in federal court would be a time to break out the popcorn.