HPV is a virus or a collection of over 150 strains of a virus. Most, if not all viruses can be found in the blood through titers but that only says there was antibodies created in response to a virus. Just because someone has HPV, doesn't mean they will get cancer, though. That's the part that seems most confusing, in explaining to others.

Oral cancer and cervical cancer can be from the same strains of HPV that are directly linked to oral cancer, 16 and 18.

So to expound upon your question, oral HPV if it is active when first exposed or until the body resolves it could probably be found on microscopic views and some lab tests but there wouldn't be any reason to do it as 95% or so will resolve by the immune system. An HPV positive tumor, on the other hand can be identified. This isn't science based, just my understanding without getting into p16 overexpression and oncogenes vs oncoproteins. That's Brian's area.