I believe it can, yes, there's some evidence that genetic change can occur throughout your life through exposure to viruses
Hold on, do you mean - in the set of all human cells belonging to an individual?

I feel like I'm reading too much into it, but I have to make sure.

So, what does make a "pure" chicken egg?
Eggs do have complex and variegated structures, so I find PVC's consideration of a chicken egg vs. proto-chicken egg to be worthwhile. That said, there's little use in considering it further unless someone manages to dig up legitimate academic speculation informed by paleontology and genetics. If not, best to leave it at:

perhaps it was a chicken egg containing a proto-chicken, a chicken egg containing a chicken, or a proto-chicken egg containing a chicken. Does the cover all the bases?