Hi, welcome to BYC!
Yes, that is my understanding as well.
I have talked with people who still have hens laying eggs at 8 years old though not as often and not as high of quality as when they were younger. Though that wouldn't be my expectation from a leghorn or other prolific layer... I recently met a guy who had a sex link still laying Silkie size eggs at 8. Another with a 6 year old Australorp laying every other day. So genetics will play a roll.
Actually unwashed eggs stay good for a VERY long time in the refrigerator. So you should be able to just stock pile enough to get you by. For example, one year I had 6 month old eggs we were eating. Only noticeable difference was the size of the air pocket. Also, they can be shelled and frozen in an ice cube tray (then bagged) for future use.
Also another way to keep winter production high is by getting a couple new birds on the year your other birds will molt. In addition you can choose breeds that are better winter layers.
So I wouldn't say by NOT letting them lay in winter but rather by not using artificial light to increase winter production and just letting their body take it's natural breaks and course of action you should definitely have chickens with longer and more productive life spans.
And I will also note that nutrition is key... like switching to a lower calcium feed than layer (usually 4%) during molt and boosting protein. Reason is feathers are made from 90% protein and the amino acids therein. So higher protein (than the 16% BARE MINIMUM) will support feather growth better. In addition, too much calcium fed to non laying birds such as those in molt *can* (doesn't mean will) suffer from kidney issues if fed long term. For this reason in addition to having multiple genders and ages, I feed a flock raiser that has 20% protein and about 1% calcium. I provide oyster shell on the side for layers. My supporting study... (one misprint say 5-17% and should say 15-17%)
http://ucanr.edu/sites/poultry/files/186894.pdf
Also have studies showing that higher protein feeds give better hatch rates and chick vitality... which to me means it MUST be more nutritious eggs! Otherwise, why better hatching/viability? Many breeders go with 20%+ and some "show" people use 25% for the beautiful shiny feathers it produces. I think it's important not to diminish the nutrition of the feed by adding in too many treats. Even though feed is made from mostly corn, it has been fortified where as scratch has not been.
Many people feed layer to all their chickens always and never notice anything wrong. I know too much and I want the best!
Again, genetics and health plays a role. So regardless of what you do they may or may not stop laying at a certain age. But giving them good nutrition and living conditions will give them their best possibility of having long, fruitful lives.
