This would be a very difficult experiment to attempt to structure and carry out, because there would be a huge number of variables that could impact the speed with which a child fell asleep beyond whether or not they were read to. Apparently you are proposing looking at a number of children, some of whom would have bedtime stories read to them, while some would not.
Variable conditions that would need to be uniform for all of the children would include the amount and type of activity the children had during the day and earlier in the evening; what, when, and how much they ate for evening meal; the noise level in the rest of the house/apartment; the temperature and lighting in the child's bedroom; other bedtime rituals (bath, brush teeth, final drink of water, finding teddy bear or blanket); and the type of story that is read and the way in which it is read (affects how the child reacts to the story, possibly prolonging awake time or falling asleep quickly).
Doing this for one particular child could be managed, at least on an informal level for purposes of that child's sleep patterns. Trying to actually conduct a large-scale formal experiment based on some hypothesis connected with this question would be extremely challenging due to the vast number of variables.