Yes I think it is unlikely and a 12ftlbs airgun would have not much power left at that range. Even FAC airgun would be pretty much useless, this is usually approx 35/38ftlbs at the muzzle.

.22RF (100ftlbs at muzzle) even 200yds is not recommended for this calibre, the sensible shooting distance would be more like 75 -100yds. The most likely small calibre at this range would be .17 HMR (Hornady Magnum Rimfire).

Any shot with any calibre on target at 200 yds is some shot! and if hunting you simply in an ideal world shoot at a more sensible range to kill cleanly.