As far as i have been able to ascertain, there is no no effect on age at start of lay.
I am saying this because what I have seen presented as the age chi kens should begin, or have begun to lay eggs. Is the same whatever the coop/ range situation.
I am not aware of any actual study having been done.
We let our chickens spend all day long outside of any coop or pen, and in a predetor proof coop at night. As soon as they are old enough to be safe. So they are inside some sort of tractor type enclosure from when they leave the brooder untill they are probably 5 weeks old. They dont sleep outside in the coop until a certain age either....but at about 5weeks they start to ne outside all day.
That's just Our house other oeople have other combos of coop time/ free time/ pen time, pastured in a tracktor...
You could do a comparison if you were very specific about your oerameters.
Just yesterday i visited a breeder whos chicks moved from brooder to a chicken barn where they spent the rest of thier lives in one of the Manymany wire oens divided by agereed/ gender... her pullets started laying,, she sad, right around 20 weeks, same.as mine.
Only our second year with chicks, but all have started to lay right on schedule.
