Inclusion of GRE score/completion on CV - under which heading?
My feeling is that unless you did phenomenally well (well within top 5%), it would not be of much relevance to those looking at your application (the likely effect would be this), and if you did do phenomenally well, then its inclusion could have the same effect as mentioning having an IQ score of 160 or more (something you'd probably not want to do, even if you did have such a score). Employers at universities or research institutions want to see evidence of teaching competence and/or research competence, not a high score on a test designed to measure your potential to do well in classwork, since presumably none of your duties will involve taking classes for a grade.