Virtually all the research says yes. It is expected that there will be measurable changes in frequency, size, and quality of egg content.
Virtually all of the research also says that those changes are likely to be unnoticable in a backyard flock, unless you routinely weigh and record all of your egg sizes, have a very large flock, and keep very good records for an extended period. They are small. Very small.
If there is a disruption in egg production, it is more likely from some combination of the sudden change in feeds (rather than the content of those feeds specifically) and the gradual reduction of hours of daylight we are seeing as winter approached.
The higher protein levels routinely recommended here by various posters, myself included, have more to do with the bird's general health and longevity than with maximum egg production at minimal costs.
4% is a big decrease in Protein. 2% is not in my experience.
I would mix the feeds 50/50 for a couple of weeks.
I changed my feed from 18 to 16% for my Hens about 2 months ago, I had no reduction in egg production till a week ago.
My 3 hens are 17 months old and molting.
Was getting 20 eggs weekly, 16 last week. GC