I am not by any means an expert in annealing, but having said that, I have read several articles on annealing, many post here on the hide, and tried working with it some myself. The gist of what I get from the research I have done is that when you over anneal, you can "ruin" the brass by making it too soft. This is most likely to give problems with neck tensions being too light, and causing bullet slippage from recoil.
It could cause a max COAL to change and cause a bullet to be jammed in the lands, with attendant pressure increases to possibly be dangerous...
I haven't read anywhere that over annealing at the neck will cause other problems---but I don't want to find out the hard way either.
In this article
The Art and Science of Annealing which I have read a couple times, and it was referenced in a post earlier in this thread, the author talks about the dangers of annealing the entire case---very not cool!
I quote a couple paragraphs here, relating to the danger aspect.
"Over-annealing is certainly the worst condition, and can even be dangerous, as pointed out above. Over-annealing has two aspects: over-annealing of the case neck only, and any annealing of the lower half of the case. There is no particular danger to over-annealing the case necks, which is the usual result of standing the brass in water and heating the necks with a torch. All that will happen is that your accuracy will not improve, or it may become worse, and the cases may seem to be a little more sticky during extraction. Case life will be improved because the necks are soft--too soft. However, you will conclude that annealing is not what it is cracked-up to be, and may even be a waste of time.
Any annealing whatsoever of the cartridge base is over-annealing and is dangerous. This area of the brass must retain the properties it had when it left the factory. If it is made the least bit softer, let alone "dead" soft, the stage is set for another shooter's nightmare. At the very least, you may get a whiff of hot gas directed toward your face. At the worst, you can be seriously injured as your gun behaves more like a hand grenade than a firearm.
I once heard a tale of a gentleman who placed his brass on a cookie tray and placed the whole batch in an oven at 650 degrees for over an hour. He wasn't hurt--at least seriously. His attitude toward annealing is very negative.
Cartridge brass which has been annealed over its entire length will exhibit signs of excessive pressure even with moderate and reduced loads. Indeed, cases in this condition are subjected to excessive pressures. Any pressure is excessive. Head separation, incipient head separation, stuck or sticky cases, blown primers, swollen cases, swollen case heads, enlarged primer pockets (I mean REALLY enlarged), and just about every other sign of excessive pressure imaginable can occur with cases which have been annealed over their entire length."
Hope that answers your question.