They may or may not use Barnes in that role. but his pre-finger slice 2021 was actually quite stellar.
It's really going to come down to how Houck and Whitlock are used. If both stay in the pen (my choice), then one probably handles the closing/high leverage and the other, along with Taylor, Barnes, Brasier, Sawamura, and maybe Valdez and/or Darwinzon Hernandez can give the Sox what looks like it could be a pretty formidable bullpen. But if one or both move to the rotation, then it puts question marks potentially all over the staff, including in the closing/high leverage role, where Barnes certainly remains a candidate.
(Of course, not all question marks are answered negatively.)