The AO is for adjusting for parallax at given ranges, and the ocular lens is to focus the reticle to your eyes despite both being called "focusing". On a quality scope with excellent glass and coatings once the ocular is set/locked it shouldn't have to be changed again no matter what range your shooting at or what mag you turn your scope to. Changing the AO to match the range is a constant chore when hunting varmints where ranges can vary shot to shot hundreds of yards. That said on lower quality scopes changing the ocular may appear to help a little with parallax, but its more likely other factors (exit pupil, eye relief, coatings, shooter technique, etc).
As already said, any higher magnification scope must have AO. Non AO scopes can be factory set anywhere from 50-150 yards I believe, and rimfire scopes even closer. They are usually not a problem past those ranges to infinity, but might be at closer ranges without AO.
A 3-9 isn't enough scope for varmint hunting in the west... even a 4-12 is borderline IMO. Kind of hard to aim and hit small if you can't see small at the longest ranges IOW. I've had times the 36X target scopes were not enough.
I prefer variables with 4-6X on the lower end, and 14-24X on the top end for varmint scopes, with AO fine CH Dot reticles AND objectives larger than 40mm.
My varmint rigs are set up for the longest PBR the cartridge is easily capable of on the game being hunted, whether rifle or specialty handgun. Means it might be 200 yards, might be 500 or 600 yards. With that on those for the longest ranges a digger at 750 or well past may not be a gimmee, but its in jeopardy.
Long range shooting is all about repeatability... the firearm, the ammo, the scope, knowing the exact ballistics of the rig with that ammo and most of all shooter technique. Matters not if all else is perfect if the trigger jockey can't consistently have the same weld, same sight picture, same technique from shot to shot.