That is a question I don't have an answer to. However, I would doubt that everyone would shut down just because one hen goes broody. I had a Wyandotte that went broody a month or so ago and everyone else pulled their weight as regards egg laying. I have 22 hens and was getting 22 eggs each day...
My Barred Rocks give me an egg a day without fail. So do my Partridge Rocks, Columbian and Silver Laced Wyandottes and Blue Andalusians. Maybe it is a competition thing with my girls. 20 hens = 18 eggs each day so someone is slacking but they probably deserve a day off now and then.
You are pretty far north so you may have to do some supplemental lighting this time of year. Make sure they have 14+ hours of light a day along with a good diet and access to calcium (oyster shell and/or crushed egg shell). You should see some eggs very soon.
That is why, as much as I want to, I don't even try to incubate any eggs. We are way out in the country on an electric co-op and we have a power outage (from several minutes to several hours) at least once a month and anytime it storms. Our co-op is really good at getting everything back on but...
I have a Columbian Wyandotte that went broody about a month ago. No eggs to sit, just broody. Prior to that she was laying large brown eggs on a daily basis. I decided to let her run out the broody thing and made sure she got off the nest a couple of times a day to eat, free range and drink...
Don't feel bad, we have all done something like that. I have had to develop the habit of, once I put everyone up for the evening, walking the entire area...in part to look for any strays that may have managed to hide and in part to look for any eggs that my ducks may have dropped and forgot to...
Just hang in there. Mine turned beat red and clucked up a storm for at least two weeks before anything happened. The first egg was barely larger than a quarter but you should have seen me dancing around like a fool. Now they cluck all morning and I just ignore them until mid afternoon when I go...
My hens produce approx. 20 eggs each day which comes out to between 11 and 12 dozen eggs a weekly. We sell a few, not many since we are 13 miles from the nearest town and folks don't seem to want to drive that far to buy fresh eggs even at 2 bucks a dozen. So, every Tuesday a.m. I take our...