I think you manage the language remarkably well.
If you want to improve the "hardness" of the clay then compost is the way to go. If you want to directly increase nutrients then compost may not provide what you're looking for. But improving the soil is always going to be a good thing whether you fertilize or not and it may be enough. Clay typically is more fertile than soils that are easier to manage. Daylilies growing in soil will not die if you don't fertilize them and it is safer to under rather than over-fertilize.