No, it doesn't affect egg quality as far as basic nutrition~same rich, orange yolks and great taste as well. Now, on the other hand, as a hen ages she may display ovulatory changes, as well as shell production changes.
Often an older hen will lay several double yolkers for several days and then stop laying for a number of days. Her eggs may be odd shaped or colored or have no shell or soft shells. She may become an internal layer and become eggbound. When these changes start, it is usually best to cull this bird as she can get into some real health problems with this....painful and life threatening.
I finally culled my ancient leghorn hen, Moby Dick, and found an enormous object inside her composed of layers upon layers of egg material. She didn't seem to be in any pain or illness but had stopped laying altogether after a few years of putting out many double yolkers.