Yes, it is possible for the school to come to a different diagnostic conclusion. They are looking at him through the lens of the school environment, while the NP most likely saw him in isolation, often from a hospital perspective. Context can be very important to interpretation. This does not necessarily mean that either formulation is wholly incorrect.
What is the primary service you are seeking? Social skills? If so, yes, that can be provided through a 504 (though some schools don't realize that). Actually, it can be provided through general ed, through a Curriculum Accommodation plan, or without any kind of plan at all (and has been, in several schools I've worked in in the past), especially if it's in the form of a social skills group (best, for transfer and generalization).
