And, assuming you do have a close enough elven donor, your freedom is probably legally fucked. It's a bad situation either way in that case, either you die or you become a slave due to having an elven relative close enough to you to be a donor, which puts your own heritage high enough to be enslaved.
Nowadays people who have had bone marrow transplants are put into a database. It's also one of the reasons why more than one DNA test type is used. While the blood may have some other DNA your hair, skin, saliva, vaginal fluid and semen would only contain yours.
Almost forgot they can tell if a person is a "chimera" from a blood test as they would see 2 different types of DNA as your own DNA would still be present to some extent. Unless they are a true "chimera" but that's a completely different thing altogether.
And no it wouldn't change your heritage enough at most by 1/8 but most likely only by 1/16. As I know a family on my reservation were the mother had a bone marrow transplant both her and her husband were born full bloodied American Indians. Her children are considered 1/32 Asian by a DNA test but that only applies if it's the mother that had the transplant because they share the same blood during pregnancy. If it was the father the children would've been full bloodied.
So even if a person was 1/4 elven they would at most only show as 3/8 still be less than half also it would be enough of a discrepancy to warrant looking into a persons medical history.