Nope, Hotchkiss was a WWI gun, the primary gun of the French army, and IIRC was actually the type used by Roland Garros. It certainly wasn't operated by the Brits in WWII, though it had sporadic use by them in the first war.

Regardless, I first learned this song from books on WWI aviation, so it was sung then, though there are WWII and modern variants. It may be based on a song about a racing driver.

A music-hall song with the refrain, "Archibald, certainly not!" was reportedly the origin of the term "Archie" for anti-aircraft fire during WWI; It was supposedly sung by pilots as they dodged ground fire, and the name stuck until WWII when "flak", after the German abbreviation for an AA gun.