Yes, sign language is used with children with Down syndrome or autism. It's used to augment the speech they have or as an alternative to speech, if speech hasn't developed. How quickly they pick it up depends on the individual child (depending on cognitive and fine motor abilities). As well, it depends on the consistency with which it's taught.
Many speech-language pathologists recommend the use of sign language with children with communicative disorders, in particular with children with Down syndrome.
I've worked with a number of children with developmental delays and we used sign a lot (with the Toronto Preschool Speech and Language Service at Surrey Place Centre in Toronto). I clearly remember one mom saying to me regarding her son's communication abilities, "It's as if he needs to see his hands make the sign, and then he can get the (spoken) word out".