Stan,
in theory this is absolutely correct.
The practical application, however, has its limits. One could kill game with a .410 as far as with a 12, if one could get a .410 to pattern as densely as the 12 (at the expense of a smaller killing circle). The "if" is a big question. I have known people who tried to achieve this pattern density with 20s and .410s, claiming that this would make their shooting more sporting. None of the attempts were successful. Besides, all experiments with extra long shotgun ammo known to me suggest that the tighter the pattern is, that is, the less space there is between individual pellets, and the more bulletlike is the pattern in behavior, the less predictable is the flight. One is bound to get problems with POI to POA consistency, for instance.
So, while the theoretical reasoning is flawless, I doubt that in real life anyone can kills with a .410 as far as with a 12 bore.