Welcome Jeff. My son is on the spectrum as well, though he is just 5 years old. I know there are people with undiagnosed Aspergers serving/ed in uniform. The rub lies in having been diagnosed. Ask the recruiter and I hope he is able to live his dream.
In many ways having Aspergers will make life in the military very difficult depending on his level of functioning and how severe his condition is. If he is unable to grasp non-verbal cues or implied meanings and takes everything very literally he will encounter a lot of problems just in BASIC training.
You might also contact Autism Awareness and see if they have any resources/advice regarding people on the spectrum serving in uniform.
"The purpose of fighting is to win. There is no possible victory in defense. The sword is more important than the shield and skill is more important than either. The final weapon is the brain. All else is supplemental." - John Steinbeck