I cannot say anything specifically about ABA, because I don't know enough about it. But I do think that people with Aspergers can support autistic people and help them to learn. I say this from experience.
Before I was diagnosed, I did some supply work at a specialist autism unit at a primary school. The teacher there thought I had a natural affinitity with the autistic children and wanted me to apply for a permanent position there, unfortunately I had other obligations at that time.
I also worked at a care home where I was able to connect to an autistic adult who didn't speak in a way that other staff couldn't. They were very confused when I made him laugh a lot- all I did was pay attention to his rituals and join in with them.
I think that one thing that I would struggle with would be applying anything that was purely done to try to normalise the autistic person. I mean, I can help them with their academic learning or teach them personal care and social interaction techniques. I would not try to suppress stimming or force eye contact, but if the person showed signs of agitation I would try to find the cause and remove it. For example, one child complained that the colour of the cushions did not match the chairs, so we re-arranged them so that they matched and then continued with the lesson.
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Your neurodiverse (Aspie) score: 149 of 200
Your neurotypical (non-autistic) score: 73 of 200
You are very likely neurodiverse (Aspie)