The screen can go black all you want, but most monitors have a tiny light that stays on whenever they're powered up. Is that true of the iMac as well?
My Mac Mini has a tiny white light that stays on, my HP monitor has a green one. My DSL router has 4 lights that stay on all the time, one that blinks, and a fifth one that I think will come on when my son connects with his iBook. My surge protector has 5 orange lights and one red one that stay on all the time, and I have an electrical adapter sitting next to the Mini that has an orange light on constantly. I do not want all these lights shining in the room I'm trying to sleep in! But, all the above are sitting on the rolltop desk. If it was in the bedroom, we could simply lower the tambour at night.
My wife's head blocks most of the light from the clock radio on the nightstand next to her, and the aforementioned answering machine display, next to me, at least faces the ceiling! ...same for the control for the mattress.