According to John McAulay in "Carbines of the U.S. Cavalry, 1861-1905" none of the Union regiments mentioned appear to have had Spencers in the summer/fall of 1864 inventory and only the 3rd Iowa in the inventory taken just before the end of the war. Very unlikely that it was Confederater captured, but certainly not impossible.

I'll get back with the specific serial number information, if any.