I'm not sure what you'd consider definitive? Yes green stems can photosynthesize so contribute some food to the plant. How much they contribute in daylilies specifically I don't know and it may well not have been studied.
Yes cutting back the foliage could have a negative effect depending how much you cut and possibly when. Basically you are reducing the area of leaf that can make food. The plant's response is to grow new leaves to get back into food manufacturing, but to do that it has to use the food it had stored before you cut it. This may not cause much of a problem except in theory with recently planted daylilies or those that are borderline hardy in your zone. We're growing them for esthetic value so sometimes we do things that are better for us than the plant
It may be that cutting back could reduce flowering the next year but whether it does is something one could test oneself. By newly planted I don't mean so recently that they are still short from transplant cutting back. Cutting back is usually necessary to reduce transpiration when transplanting, which is potentially more serious than temporarily reducing photosynthesis.
Yes nutrients are recycled back to the plant from dying daylily flowers. This has been studied in scientific research. I can give you the references but not until tomorrow.
