I've been researching the line of John Adams, carpenter of NU Co with wife Katherine for quite some time now. We now have several descendants with a DNA connection and a documented descent from that line. They are not connected with the MA Adams family at all. The evidence regarding Gabriel is equivocal. One man who claimed descent from that line failed to match the NU / Stafford Co Adams at all; nor does he match any other participant. Despite several requests he has not responded to requests to share his lineage with other researchers so that it can be determined if he has made an error in his descent chart. Thus far, no other Adams-surname males claiming descent from Gabriel have come forward. John Adams, carpenter, with wife Katherine is almost certainly the son of Dr William Adams, of NU Co, who died in 1657. His father had brothers Thomas (a bachelor) and John (later found at Lancaster Co)as a neighbor to William Feathergill. John Adams, carpenter, appears also to have had a brother William (d 1677) whose young widow Frances married "old" Richard Routt and went on to have four children in the 1680s and 1690s (i.e., she was more or less a contemporary of John Adams, carpenter).
We are able to identify a great many possible children for John Sr but able to confirm only John Jr whose third wife was named Elizabeth (but not Elizabeth Johns). William Adams of Kettle Creek, George Adams of Broad Run, and John Adams III (with wife Eleanor), later of Halifax Co are likely sons of John Adams Jr by an unknown first wife. Nipper Adams, named in the estate settlement for John Adams may be a child of this couple as well. He is not, however, the man of that name who married Lucy McKendree ... that man is a much younger orphan Nipper Adams b ca 1745, whose guardianship is contested at PWCo by Richard Adams, another son (or possibly nephew) of John Sr.
Those who have tested in this family include a direct descendant of John Adams III and wife Eleanor of Halifax Co, a descendant of John "Hobbs" Adams later of Wilkes Co NC, a descendant of Daniel Adams, the youngest of five brothers at Goose Creek, a descendant of William Adams (son of John and Eleanor) and two descendants of Absolem Adams of Fauquier Co, who married into the Feathergill family.
Whether we can confirm a relationship to the other Adams-surname men of Virginia's northern neck rests on whether someone claiming descent from any of them matches the DNA. This family is family 023 on the Adams-surname DNA results page.
As to your lineage, with those names there can be little doubt that you descend in the line of Gabriel Adams and wife Priscilla Pearson, and I would certainly make that my starting point. The lack of a headright or other immigration listing for Gabriel certainly seems persuasive of his descent from an already extant family.