William,
It would be so wonderful if the family trees could populate based on our DNA information. I think the only thing we can do at this point using the DNA information we add to Wikitree is to help cousins find us who believe they are connected through the same ancestors. They then can test their DNA against us and see if there is a match, and we can compare information.
I have read that DNA doesn't get passed along equally, so beyond really close relatives, you can't definitely say that someone who doesn't match isn't really a blood relative, although you can say that people who match beyond a certain small "noise" level really are our relatives. (I think).
I don't have experience with GENI. I think there is probably a way to download the family tree information from GENI into a GEDCOM, which can be uploaded into Wikitree. Even this GEDCOM upload process has changed since I did it -- and I don't think "upload" is the correct term anymore, since you have to go through a screening process to ensure you're not adding duplicate people who are already on Wikitree...
Maybe it would help to ask your question (as a new question) about GENI, (and put the words GENI and GEDCOM at the bottom as tags) .. and that should get the attention of the people who know more about the process and can really help. Since we are only "commenting" at this point, this question won't be refreshed, so it may escape notice.
Reba