The Online Etymology Dictionary suggests:
conk (v.) as in conk out, 1918, coined by World War I airmen, perhaps in imitation of the sound of a stalling motor, reinforced by conk (v.) "hit on the head," originally "punch in the nose" (1821), from conk (n.), slang for "nose" (1812), perhaps from fancied resemblance to a conch (pronounced "conk") shell.