Sort of, and months rather than years. From Wikipedia's page on Utah (http://en.wikipedia.org/wiki/Utah):

Brigham Young and the first band of Mormon pioneers came to the Salt Lake Valley on July 24, 1847. Over the next 22 years, more than 70,000 pioneers crossed the plains and settled in Utah...

In 1847 when the first pioneers arrived, Utah was still Mexican territory. As a consequence of the Mexican-American War, the land became the territory of the United States upon the signing of the Treaty of Guadalupe Hidalgo, February 2, 1848. The treaty was ratified by the United States Senate on March 10.

The war started in 1846, so the first Mormon settlers were actually crossing the border of enemy nations. Except neither country was actively administering the area, nor contesting it militarily.