Absolutely. To give only the most obvious example, the United States fought concurrent wars against Native American nations across the Great Plains during the Civil War. The Cheyenne, Sioux, Shoshone, Apache, and other nations all attempted to gain an advantage from the distraction of the Civil War.

The Comanche raided Union-controlled New Mexico as well as Confederate Texas. The Comanche profited from their hostility to Texas as well as the war-weariness of the United States; in 1865 the U.S. government recognized for the first time a Comanche homeland, legally comprising the western half of Oklahoma and 40,000 square miles of western Texas. (Of course, the government quickly signed another treaty in 1867 stripping the Comanche of ownership of land in Texas, and continuing war forced the Comanche into nearly total surrender within a decade.)

Juan Cortina, who rose to prominence as a bandit/outlaw in Texas before fleeing to northern Mexico, embraced a new position as a military leader during the French invasion of Mexico. As the commander of Mexican forces near the threatened Union outpost of Brownsville, he profited from smuggling and intelligence work, and actually fought alongside Union troops against Confederate forces in September 1864. Cortina would, before the end of the war, reinvent himself as a royalist before again taking up arms as a Juarista warlord and skimming the profitable customs revenue from the port of Matamoros (with covert assistance from the U.S. government). Cortina would eventually squander his goodwill with the U.S. government by continuing to rustle American cattle; the new president Porfirio Diaz arrested him in 1876 to curry favor with the Americans.