Does having an abscessed tooth affect vision?

Not normally: Perhaps if the swelling was so bad that the eye became shut or if pain caused excessive tearing, it might affect vision. It is normally not related.

Rare, but possible..: An odontogenic abscess (abscess from dental infection) may involve the maxillary sinus which is just below the orbit or bony skull structure that contains the eye. Unchecked, the infection can progress to an orbital cellulitis, which is a medical emergency and can result in of vision. This has been documented before: http://www.Ncbi.Nlm.Nih.Gov/pubmed/17561769.