It took me quite a while to find this guy, but yes, there was one! Peter Conover Hains was a West Point graduate born in 1840. He was commissioned in the Union army in 1861 as a second lieutenant and served variously as an artillery officer and a military engineer, seeing action at both Hanover Courthouse and the Siege of Vicksburg, and ending the war with the rank of lieutenant colonel.

He remained as an engineer with the army after the war, and was involved with (among other things) the construction of the Panama Canal. He also fought in the Spanish-American war as a brigadier general. In 1904, he reached the mandatory retirement age (64) and was forced to leave the army. However, he was recalled during WWI (at age 77), and served as an engineer with the army until 1918.

EDIT: I've been reading some more, and apparently this guy actually fired the very first shot at the Battle of Bull Run, designed the plans for the entire Siege of Vicksburg when his superior officer got sick, served in over 30 battles throughout the Civil War, and was a classmate of George Custer. Also, there's currently a big statue of him at Vicksburg. As far as I can tell, he's 1860s Forrest Gump.