Assuming he really does have ADD, the most frequent co-morbid issues are:
1) motor skills - fine and/or gross (can be one without the other). This would be an Occupational Therapist (OT) evaluation, and the school's level of evaluation is not detailed.
2) LDs - very common, and yes, school "should" be able to test for these. Accuracy/validity depends on the qualifications of the tester and the attitude of the school/SD. If they are honestly wanting to deal with LDs (and some school systems DO take LDs seriously), school testing will be useful.
3) might not hurt to rule out Auditory Processing Disorders (APD), especially the lessor known ones like "auditory figure ground" (problems filtering out background noise). APDs can look like ADD... or it can be both.