Family Tree DNA has about 398 Adams DNA tests in their Adams family Project. They have sorted the resullts into various family groups. Some of the families have documented genealogies that go back to Europe.
If you have a male Adams relative, It may be worth while to have a test done. The DNA test might identify whether you are "decended from", "related to", or 'not related" to the Presidential Adams family.
My Adams family turned out to be "related", not "descended".