No. The 1867 Alaska Purchase (Treaty of Cession) was a purely diplomatic transaction. The United States bought Russian America for $7.2 million. No military conflict occurred between American and Russian forces in the region.
Russian presence in Alaska was primarily through the Russian-American Company (fur trading). By the 1860s, Russia—facing financial strain and fearing British seizure of the territory in a future war—chose to sell. Negotiations were conducted peacefully between Russian diplomat Eduard de Stoeckl and U.S. Secretary of State William Seward.