There is a Nelson listed in Brittain's will, according to the Duke-Symes book. The next couple of pages mention a Nelson who was a minor orphan of Brittain. I am not sure about the accuracy of that book, but that seems to be where the notes on FamilySearch came from. Here are the pages where Nelson is mentioned:
There is a Brittain descendant (through Dabney) in the Duke Y-DNA study group, so we know he came from John Duke of Isle of Wight. I'm a co-administrator in the group, and we've tried to contact him to upgrade for more detailed testing, but he has been unresponsive. I am not aware of any Nelson descendants in the group, but If there is a male still carrying Nelson's Y-DNA, that could help prove the connection to Brittain.