stillcrazy,
You ask, "Does it really do what they want it to do?". I'm assuming "what they want it to do" is the relief of residual stresses.
It would all depend on the prior processing. A stress relief operation will lower the residual stresses, if present, and, yes, a two hour stress relief at 1135-1165 F (which is 1150 +/- 15F) for two hours would be effective at relieving stresses. I doubt such an operation would adversely affect the mechanical properties of the material. Of course, if the residual stress level was low to begin with, the benifit would be small.
Could you "get away" with eliminating the SR operation? Perhaps, particularly if the forged ring was properly solution treated and aged after forging and no straightening or cold working was performed. A lot would depend on the dimensional requirements of your finished part and the cost of re-processing and or scrapping if re-processing is not applicable. But, since the cost of SR is relatively low, it is viewed as cheap insurance. It can also eliminate the machinists' most common excuse ("the material moved") for missing tight dimensions.
If you wanted to save money on processing, perhaps you could bring the rings in as Condition A (solution treated), and age them after rough machining, with what would amount to the exact same treatment as your SR treatment. I don't know what specifications you are working to, however, so this might require additional mechanical testing.
rp