Second grade is still a fairly flexible grade. Third is the worst since they are tested for the first time. Look into how third grade works at your school. Many just focus on the standardized tests. This is when many students begin disliking school.
If you can work second grade to let him excel - especially in writing and then skip to fourth, I'd do it. Often teachers 'get' to teach second and newbies 'have' to teach third.
My daughter spends three month of the year testing and she scores very high. In seventh grade, she began having anxiety over the tests - bad attacks. I think she wants to do so well on them that she makes herself sick. We do not push her. She went down 5 points in English in seventh (although she scored at a twelfth grade level) and she really got upset.