Yes, by all means keep him home! If he is feeling psychologically unwell, then he is unwell! (although if the one piece he is missing is the classroom observation I imagine keeping him home will delay results even more.)

If you decide to give up on the schools evaluator, I will also recommend the Yale Child Study Center in CT - I was shocked at how fast we were able to get testing done for our daughter - but I will warn you that it costs an absolute fortune.