No doubt, a natural water content near LL ordinarily occurs in material with low OCR, but it isn't necessarily so by principles of soil mechanics. As written, your post looked like a blanket statement that LI of 1 implies OCR of 1. I don't think you can even make the generalization that the settled water content is close to LL, especially when dealing with material containing montmorillonites, attapulgite, etc. For those, the settled water content can be a lot higher, and you don't find Wn=LL until pretty deep below the mudline.
In theory, you'd have to consolidate to Wn just below LL to have Wn=LL after unloading. In reality, the amount of rebound after unloading of such soft material is pretty small. It's not zero, but can be neglected within the precision that we can hope to achieve outside the lab.
If the water content > or = LL, it probably doesn't matter what the actual OCR is - it's soft, weak, and highly compressible regardless of OCR.
DRG