Yes, that's Dr Osamu Hotta's theory, which is detailed in
this PR thread.
Dr Hotta says the ME/CFS-like illness that can (very rarely) appear after HPV vaccination can involve chronic nasopharynx inflammation (inflammation that he believes the vaccination can trigger). This illness is more ME/CFS-like than true ME/CFS though.
I am not sure if there is any infection in the nasopharynx in these patients, or whether it is just inflammation (like autoimmune inflammation, without an infectious case). Dr Hotta treats the inflammation with topical zinc chloride applied to the inflamed area, and in some case has obtained dramatic remissions.
Dr Hotta said he has also found a few cases of true ME/CFS triggered by vaccination involved chronic nasopharynx inflammation and responded to his treatment. Though I was in contact with one mother whose daughter developed an ME/CFS-like illness after their HPV vaccination, and there was no sign of nasopharynx inflammation in this patient. So this theory may apply to some patients, but not others.