The health of the plant will not suffer by not deadheading and allowing seed production. That is what flowering is all about so it is normal. What will happen is that the plant will have less "food" that it can store because it will have been used for the seeds. What effect that will have on the plant depends on where it is being grown and how it is being grown. If it is fertilized well, watered well, temperatures are not too hot, there is not a lot of competition from other plants, it is not too large a clump and so on then the difference between deadheading and not deadheading may not be noticeable.
Most cultivated daylilies do not produce many seeds naturally. So deadheading most flowers will not usually remove many, if any, developing seeds because there may not be any. Some daylilies, such as the small-flowered rebloomers like 'Stela de Oro' do have seed pods naturally. So, to some extent, it depends on the actual daylilies. Diploid daylilies may set more natural pods than tetraploid daylilies theoretically but there is no objective information about that.
So if you have daylily plants that set a lot of pods naturally (visible after the dead flower drops off or dries and is removed) then deadheading the pods may be worthwhile.
Daylilies destroy their flowers on purpose. When they do so they scavenge material from the flowers to use for growing more flowers, for storing, and so on. If a flower has not set a pod then it is not making seeds. Removing those flowers too early as
@Sooby indicated will be removing material that the plant could have used for new flowers, leaves, storage for use the next spring, etc.
