I think I'm a bit confused about what is being asked. When I read the original question, I was interpreting it to mean:
If I choose x oil in my soap for x benefits will it remain in the soap?
A specific example: If choose avocado oil in my soap for the beta carotene, protein, lecithin, fatty acids, and vitamins A, D, and E to help moisturize and protect skin from damaging UV rays and also increase collagen metabolism, will those benefits remain in my soap?
This comment from OP is confusing. Coconut oil
before saponification does not lather. That is the benefit of using coconut oil in soap, the result of saponification is that coconut oil soap is water soluble and creates lather faster than other oils. However, the comment about avocado oil being nourishing is what I read as a before saponification statement.
The way that I have approached formulating my own recipes is to look at various charts to see what affects the oil has to the soapmaking process (slows trace, speeds trace, bar hardness, lather performance, etc) - rather than looking at oil properties BEFORE saponification. I haven't been convinced either way if vitamins etc survive the lye monster or not, so I don't choose oils for those properties.
This is a chart that I particularly like, it helped me when experimenting with formulas, but it still came down to having to try things in small batches.