I'm thinking about throwing PA 3x prism on one of my ARs. One of the benefits aside from magnification is an etched reticle. If for some reason the reticle can't be illuminated, how difficult is it to utilize the BAC  for CQB situations?

It can be quite a bit harder.  I've used it with a TA01NSN a few times and it definitely didn't feel as fast.  I'd say it really depends on the reticle.  The long crosshairs of the NSN did help sort of "draw" my eye to the center.  I'd imagine a small unlit floating reticle would be even more difficult.

The Bindon concept pretty much relies on a STRONG contrast between the target and the central targeting element. Some people can shoot fast with both eyes open with just an unlit duplex, but not many and almost certainly not NEARLY so fast as with a bright central element.  Training helps but a small, bright dot seems to work best for most and be learned fastest by most. An unlit central element works just okay if it is bold, simple, and contrasts well with the target. Works very poorly in low light and no good at all in the dark.

I couldn't really do the BAC with a fiber optic ACOG.  I kinda could, but couldn't really hit shit.

I did better just point shooting.  Did a lot better with a 1-4, which I still use.

The problem people have shooting both eyes open through a 3.5x ACOG is the 3.5x part. It's much harder to do than with a 1x optic or something very close to 1x. The brain has trouble merging the magnified view from one eye with the non-magnified view from the other. It makes some people sick to their stomachs to even try, especially when moving.  It was mainly for this reason that Trij starting offering the ACOG with an RMR piggybacked.