It might, but you would need to track down a heritage breed. Modern chickens have been selected to grow big and fast. They also lay eggs FAR faster. This, unfortunately, lowers the quality of individual eggs. Poor diet and conditions reduce this further. Home raised chickens fix the diet and conditions, but still use fast laying breeds.

Alternatively, duck eggs tend to be a LOT better. They have not been as heavily selected for laying speed. They also, naturally, have a more intense yoke. I grew up in a pub, in my youth. It took a while, but the customers eventually made the connection between our unusually tastes pies and pastries, and the pair of ducks living in the gardens.