If a WW2 pilot shot down a V-1, did that count as a "kill"? Could a pilot become a flying by shooting down V-1s?

Claims against V-1s (often known as "Divers" from their codename) were counted separately from aircraft; you can see the different markings being applied to Sqn Ldr Horbaczewski's Mustang here, black crosses for aircraft, swastikas with a V-1 silhouette for divers. Pilots with five or more V-1 claims are generally specifically classified as "V-1 aces" - e.g. Christopher Shores has a separate chapter, "Diver - The V-1 Aces" in Aces High, and writes "[V-1s] were not counted as enemy aircraft, and were not therefore added to victory totals. (...) Other pilots destroyed five or more V-1s, but did not shoot down the required number of aircraft to be included [in the biographical section of the book]".

That said, there isn't really an official definition, the RAF don't formally recognise an "ace", so the "V-1" qualifier might be dropped when referring to someone like the French pilot Jean Maridor, credited with 11 V-1 victories though only three against aircraft.