I did a small test with an unmaxed weapon on ambus today and updated
my earlier post with the actual data. Lots of uncertainty, but for what it's worth here is a chart with the summary so far of all my tests.
I'm still seeing a lot of variation during a test, and several misses in a row or on one mob. I was much less careful in this test than the previous: i tagged the ambu without counting the shot(s) to discount lagged mobs, and once it was headed toward me i started counting.
I tried changing the conventionally accepted hit % range (80-92) to 80-91 because i always got around 9% misses with the maxed weapon, but the unmaxed values fit much closer if i kept the old range.
This uses a range from 81 to 91 hit%. While the higher effective HAs come closer, the lowest is farther away so i'm not sure this is the right way to do it, either. I don't consider my data accurate or confident enough to justify either of them
Results seem favorable for attachments raising the effective hit ability on unmaxed weapons, but i'm not fully convinced. Call it 50:50.

I don't see any way to include the tt of the attachments (Recodo's initial post suggested that the condition of the attachment plays a role) and get sensible results though. I'd guess the attachments contribute full mod % until broken completely. Having not broken an attachment i don't know if you can even put it on the weapon when broken, anyway.
It seems pretty clear they don't do anything significant on maxed SIB weapons. I guess my earlier observation was a coincidence after all. Eerie.