This sounds a lot like the school that my daughter is in - CogAT is the qualifier, and they won't take private testing. I wouldn't test him now, but I would enroll him at the magnet school, just for the convenience factor. For what it's worth, DD had no real problems changing schools in 2nd grade - she had new friends within the first week. It's easier to do the younger you are.
On the other hand, if outside testing would actually qualify him for the program, I'd have him tested. But if you'd be doing it just for information, I wouldn't bother.
