My impression is that CMSIS was designed to be a layer (API ?) for cortex, but it looks like not all chip makers follow this idea.
I've seen STM, and arduino alike Maple (STM32F103) project was completely build on CMSIS, but it isn't the case for Atmel.
He invented ASF, and I don't know where you find ADC implementation in CMSIS, but what I can see in my arduino installation, all hardware API calling to ASF, leaving to CMSIS just headers and registers definition, as already noted above.
http://asf.atmel.com/docs/latest/architecture.html
http://asf.atmel.com/docs/latest/sam3x/html/group__sam__drivers__adc__group.html