George Soule, "Mayflower" Passenger - DNA

Interesting. I am a member of the Descendants of the Mayflower, and George Soule is my ancestor. I was vetted pretty rigorously to be accepted. My DNA is with Gedmatch so I should share DNA with this person. I wonder if I should attach my DNA. First I would have to figure out how to. It is a pretty ancient ancestor so I could be a 7th or 8th cousin and may not show anything.
Any recommendations, feel free to share.
Tom DelGiorno