So the question naturally arises as to whether or not the mainstream Church of Jesus Christ of Latter-day Saints would reinstitute the practice of plural marriage should it become legal in the United States. LDS officials have not addressed this question publicly, but the question is explored by Salt Lake Tribune reporter Peggy Fletcher Stack in an article entitled "Will polygamy return for LDS here and hereafter?". She cites Brigham Young University political science professor Valerie Hudson, who opines that even if plural marriage was to become legal, that doesn't mean the Church would reinstitute the practice. Hudson focuses her analysis on LDS scripture, most notably Doctrine & Covenants Section 132. She interprets Joseph Smith's analysis in Section 132 to mean that Mormon polygamy was an exception to the eternal principle of monogamy, and it was removed when the sacrifice no longer was necessary.
What also must be considered is the intended targeted audience. Doctrine & Covenants Section 132 was deliberately directed towards Latter-day Saints at the time. In contrast, there's a contrasting scripture in the Book of Mormon that was directed towards a DIFFERENT targeted audience -- Jacob 2:27, which is replicated below with surrounding verses to provide context:
23 But the word of God burdens me because of your grosser crimes. For behold, thus saith the Lord: This people begin to wax in iniquity; they understand not the scriptures, for they seek to excuse themselves in committing whoredoms, because of the things which were written concerning David, and Solomon his son.
24 Behold, David and Solomon truly had many wives and concubines, which thing was abominable before me, saith the Lord.
25 Wherefore, thus saith the Lord, I have led this people forth out of the land of Jerusalem, by the power of mine arm, that I might raise up unto me a righteous branch from the fruit of the loins of Joseph.
26 Wherefore, I the Lord God will not suffer that this people shall do like unto them of old.
27 Wherefore, my brethren, hear me, and hearken to the word of the Lord: For there shall not any man among you have save it be one wife; and concubines he shall have none;
28 For I, the Lord God, delight in the chastity of women. And whoredoms are an abomination before me; thus saith the Lord of Hosts.
Verse 1 indicates that Jacob, the brother of Nephi, directed this counsel specifically towards the people of Nephi. And this counsel also held firm for Mormons until such time as the Lord directed DIFFERENT counsel towards them, as codified in D & C 132. And the counsel in Section 132 remained in effect until the Lord once again directed DIFFERENT counsel towards Mormons in 1890, when by revelation He authorized President Wilford M. Woodruff to indefinitely suspend the practice of plural marriage. The 1890 Manifesto is canonized as Official Declaration 1.
Our Heavenly Father never actually changes His mind, though. Instead, He changes His perspective on how much power and authority we can possess and handle. When He decided that some people could handle plural marriage, He permitted them to adopt it. But in other circumstances, He decided that "His" people could not handle it, and so He forbade it. That's how the Father works -- and He communicates His desires through the principle of continuing revelation. It is our belief in the principle of continuous revelation that distinguishes the LDS Church from most of traditional Christianity.
Thus we can safely say that even if plural marriage is legalized in the United States, the Church of Jesus Christ of Latter-day Saints will NOT reinstitute the practice unless permitted by revelation to do so. Revelation intended to apply to the entire Church means that the President of the Church receives it, presents it to the Quorum of the Twelve, and once each member of that Quorum receives the same witness, the revelation is then presented to the membership for a sustaining vote, after which it is canonized. Of course, this would present the dilemma of the Church refusing membership to those who legally marry more than one wife, but the Church has established a precedent by currently refusing membership to polygamists even in countries where plural marriage is legal.
The Tribune article also brings up some additional Mormon beliefs involving polygamy, particularly the fact that many Mormons believe plural marriage will be practiced in the Celestial Kingdom. These beliefs are supported by the contention that more women than men will qualify for celestial glory with exaltation, and if marriage is required to gain exaltation, and more women qualify than men, then provision must be made for the surplus women to satisfy the demands of eternal justice. This implies that some men will end up with more than one wife. However, this is not an official doctrine of the Church, and so it remains speculative.
I personally believe that plural marriage is currently practice in the celestial kingdom, but I speak only for myself. A verse in Isaiah 4:1 seems to give some support to the possibility; it states "And in that day seven women shall take hold of one man, saying, We will eat our own bread, and wear our own apparel: only let us be called by thy name, to take away our reproach". While the specific number "seven" appears to be symbolic, the message is that plural marriage will exist. In JosephSmith.com, the opinion is expressed that this might better apply to the earth at the dawn of the Millennium to counteract the expected numerical deficiency of men after the wars and judgments of the Tribulation.