In regard to neck tension after or before annealing, it is often quoted that annealing reduces neck tension, which is true, although springback is actually INCREASED. This is where the lines are often blurred because the wrong information is put out there so often. Many believe springback is REDUCED by annealing, this is not true. Springback in hard brass is almost non-existent, which is why it is harder to size and it is prone to cracking.
Neck tension is also believed to aide in bullet release by many, again, this is untruth. Neck tension changes start pressure by a fraction of a second, once the case is pressurized by the primer flash, the case is already starting to expand at the neck. This is also why factory ammo is crimped 99% of the time, the change in start pressure is beneficial in making the ammo have small SD's, generally speaking. Obviously not all factory ammo produces good groups in every gun, but it is often more than not that it does.
This is easily seen when fire forming cases and a less than ideal charge is used, the forward half of the case is expanded to the chamber, while the rear of it stays the same.
The neck expands first and easiest due to it's thin construction. Bullet release happens when the neck expands, not from the drag imparted when the bullet was seated.
Another misconception is from bullet runout changing after annealing, yes it does, but does it change anything on target?
I tested this in a comp barrel in 300WM with 210gr Berger VLD's, even .008" runout didn't effect on target results, it stayed the same with a tuned known load.
The throat controls bullet alignment, not the neck, it can't, it has already expanded releasing the bullet even before the bullet hits the rifling.
As to annealing after sizing, I see this as reducing neck tension due to softer brass, nothing more.
I have always annealed before sizing, after cleaning and trimming, if necessary.
I think I will try a batch of 20 of each and see which, if any, change on target results.
Cheers.