In Scotland, or at least Edinburgh, probably not, unless the Aspies were able to hide their Aspergers REALLY well. The social services are both incredibly strict and incredibly stupid. It doesn't stop children going to bad homes- I knew a girl when I was a child who was adopted by a couple who my parents met and reckoned there was something far wrong with them. They seemed to want to have "perfect" children, and whilst the girls brother seemed able to do this, the girl wasn't (I'm not sure how, she never talked about it). They got "tired" of having her and basically neglected her. She was very needy and clung to anyone she could call a friend. By the age of 11 she was sleeping with the boys in the gang, and by her mid teens was pregnant and homeless, and was taken back in by the social services.
One of my mums friends used to foster children but gave it up thanks to the social services' adoption policy. A 10 year old boy moved in to her house on a temporary basis. He was troubled but was actually a very nice kid. The short term stay became long term, and he settled into her family and neighbourhood, settled at school and was essentially her adoptive son. When it became certain that he couldn't return to his birth parents, by which time he was in his mid teens, he was put up for adoption. My mums friend immediately applied to adopt him- it was the most obvious thing in the world to her, her family, and the social workers looking after the boy. Her case was refused point blank without any consideration by the people further up the heirarchy. Why? The boy (young man by this point) is black, she and her family are white. On a happier note, he moved back in with her when he was 18 and legally an adult.
So, in a nutshell, to adopt in Scotland at least, you'd need to convince the social services that you conformed to their notion of perfect parents (whatever that may be), you'd have to conform to whatever rules they had written down in front of them (i.e. be the same race as the kid you wanted to adopt), but once you got the kid you could pretty much do what you liked with them and no one would care.