YES YOU CAN
Yes, it is certainly possible, here is an API for that:
https://market.mashape.com/ehmo/savedeo
While it is against YouTube Terms of Service, it is technically possible to hack your way to the audio-only download link, and that’s how the API’s above work.
The is how I imagine the SaveDeo API does its magic:
Download ONLY audio from a youtube video
This is what the guy at SaveDeo told me:
Youtube has audio only files. Savedeo doesn’t do anything beyond
providing you with the link. How we’re doing this is the reason why
are you using savedeo, isn’t it.