I think the biggest factor will be who else is in the lineup. As of now, the team is incomplete.
When the Sox had Ortiz and AGon, they had to get creative to get both bats in the lineup in NL road games. But this team right now has no such problem. The internal candidates at 1b are Chavis and maybe Dalbec, and benching either for 9 games doesn't look like a big issue. In the outfield, Bradley is reportedly gone, so there is a huge question mark in CF. If Betts is also gone, that doubles the questions. The Sox don't have much in the way of internal solutions - Durran, Wilson and maybe (but probably not) Castillo. And the only external name mentioned so far (Jake Marisnick) doesn't represent a massive change in this status. If any of them were benched to put JD in the outfield for 9 games, I don't see that being a major issue. Even a worst case outfield of Martinez-Benintedi-Betts might have defensive issues, but that hardly guarantees losses every time they send them out there.
If JD plays the field in NL road games, where he plays is likely to be determined by whoever fills out the outfield and who winds up holding down 1b...