The downside is that if another evaluator wants to use the same test, they can't. You cannot redo the same assessment unless it's been 12 months. With an ASD identification from the school, he will get more appropriate to ASD support. The support you provide w/ ASD is a bit different from DS alone.
When you go to apply for SSI or a waiver, having the ASD dx will open up a few extra options. If you do not have an appointment for an ASD eval outside of school, I'd be OK with the school doing these assessments.