I have planted pepper and tomato seeds on a heated surface to help them sprout, I have never used a heated surface for daylilies that I can recall. I will say I don't do it anymore if I ever did. But not saying that it would be a bad thing.
I personally would not wait till green leaves are showing, I want to get the germinated seeds under light as quickly as possible just to avoid any chance of them getting tall and thin trying to find light. I am forgetful and life happens so they might not get any attention some days. I want them to be like pepper and tomato plants...stocky and not spindly (thin and weak). So my lights are set right above the cups so the light is available as soon as the leaves break the surface of the soil. Is it safe to wait until green shows...I think it is safe, but you would just have to be careful just like you would have to be when the first root sprouts show so that it is not broken off when transplanting. That is why I like to plant my seed in cups and cover them before they sprout. I don't always manage that because sometimes they actually sprout early in the little baggies. I have over looked some sprouted seed and some that had green showing and they did just fine. If a person is limited for space under the lights, I could see waiting till roots or greenery appears, that way no space is wasted on space that may not even produce a sprouted seed. But people who do that might have some other reasons, I don't know of any reason that would be better, but people have reasons for doing things
Edited to add:
Commercial growers use green houses for a reason, our guest speaker at our club meeting this week was from Georgia and he has a friend with a large green house. The friend lets him grow his seedlings in the green house and instead of having to wait two and maybe three years for a bloom he gets a large majority of bloom now in one year. So maybe not a heated surface but certainly growing under controlled temps helps speed up the process. Of course in the green house the watering and the fertilizing along with the temperature is well managed.