It doesn't take the 1st-level druid spell magic fang [trans] (Player's Handbook 250) to make a monk's unarmed strike into a natural weapon. The monk class feature unarmed strike, in part, says
A monk’s unarmed strike is treated both as a manufactured weapon and a natural weapon for the purpose of spells and effects that enhance or improve either manufactured weapons or natural weapons (such as the magic fang and magic weapon spells). (41)
That said, it's totally legit for a monk to wear, for example, +5 disruption speed bracers of striking (Magic of Faerûn 155–6) (400,000 gp; 0 lbs.) and a +2 anarchic flaming frost shock thundering unholy necklace of natural weapons (one) (Savage Species 58) (200,000 gp; 0 lbs.) and have his unarmed strike benefit from both items' magic weapon special abilities. You're right, of course, that the items' enhancement bonuses will overlap—not stack—, so the wearer of both only gains a +5 enhancement bonus on attack rolls and damage rolls, but, yeah, all of the magic weapon special abilities will function normally.
Keep in mind, though, that investing in both bracers and a necklace is tremendously expensive—approximately equivalent to three magic weapons, (Finally a more expensive fighting style than two-weapon fighting!) At the game's end, a level 20 PC's entire outlay for gear is only 760,000, and a suite like the above just can't be afforded before then. Still, prior to attaining such dizzying heights, there's undoubtedly a mathematical span during which it's optimal pricewise to have magic weapon special abilities spread out among both bracers and a necklace. However, even if that span's functionally forever, don't think it will have long-term impact on game balance (such as it is). For example, the combination of bracers and necklace may make it so that the monk's unarmed strike is perpetually one or two (and, yes, eventually, nine or more) magic weapon special abilities ahead of the barbarian's magic axe. That's weird, I guess, but were I the barbarian I think I'd be happy for my monk buddy—he needs all the help he can get, especially since most of his funds are sunk into those bracers and that necklace.
Note: There are ways to get more magic weapon special abilities on a natural attack or unarmed strike; see here. Also, the game doesn't limit this let's-put-more-thing-in-that-thing stuff to magic weapon special abilities. Magic armor special abilities can be added to magic armor, bracers of armor (see here), and the chahar-aina and dastana, and all of those can be worn at once. The enhancement bonuses won't stack, but all the compatible magic armor special abilities work normally. Heck, you can even carry a shield or six to get still more.