William W. answered 02/21/22
AP Biology teacher with molecular genetics experience
This question is almost as interesting as "if 1 set of identical (monozygotic) twins has children with another set of twins (also monozygotic), will their children be identical?"
The short answer is, unfortunately, no giving birth to oneself. This seems less of a practical genetics question than an anatomy anatomy and physiology one. Bone marrow is primarily responsible for the production of blood cells which are not directly involved in reproduction. It appears that bone marrow recipient is biologically female as they are the one who the question asks us to think about giving birth. With that in mind, it's important to recognize that all of a biologically female person's eggs are formed while they are in-utero, BEFORE (their own) birth. This is years before most bone marrow transplants. Though this person does have cells containing DNA from two individuals, their eggs only have their genes.