It matters if he was recorded as Bottom or Bottoms: if he was only recorded as a Bottom then there is no way to know whether or not he was from a Longbottom family. If Bottoms, then likely so. There were and are Bottom families not descended from the Longbottom families.
The Nash Co NC Longbottom/Bottoms family was strongly associated with the Joyner/Joiner family, including a Burrell/Burwell Joiner/Joyner, so that might be a clue.
The family was also closely associated with the Kersey family who moved to Bladen Co NC in 1760s-1770s.
Please let know if Joiner/Joyner or Kersey showed up in any of your records.