I have always thought that the bracers were enhancement bonus, for some reason. However, I am not sure you can claim enhancement bonus from different items. Otherwise, wearing a leather armour +3 under plate armour would give you an AC bonus of +11, which shouldn't be how the thing works.
Provided that the plate armor you're wearing is not magic in any way whatsoever, since they occupy the same slot (and would thus
suppress if magic), there would be nothing preventing such use (in 3.5/PF). However, talking about Bracers, since they expressly occupy different slots in terms of magic items, would be able to have Enhancement Bonuses that would not interfere with whatever you're getting (or not getting) from an Armor (as long as it's not an enhancement bonus to the same thing).
In PF, this is even explicit (whereas in 3.5 there's just nothing preventing it, AFAIK), and you can put different kinds of armor enchantments/improvements/special abilities on your armor and on your bracers (of armor) and have them stack. This can lead to some oddities, but nothing out of the ordinary when dealing with 3.PF, which is why DM arbitration exists. It could get costly, though, considering that they need to be magical, with enhancement bonuses not stacking, meaning that almost no matter what, +1 enhancement armor bonus would be "wasted", either on the bracers or on the armor.
In 2nd Ed, they just straight up give you the AC as stated, just like normal armour.
Well then the IE games all "fucked up", because Bracers of Defense do not stack with armors in any of them.