Yes. I've done this a hundred times.
I use
http://www.youtube-mp3.org/
a website that does not contain any spam or viruses. It's just a website. You don't need an account. You just open the website up in one tab. Open the youtube up in another tab. Copy the url of the youtube that you like, say....you like the official video for a current 'hit', and you want to audio for that hit, without the video.
So you copy the url, and paste it into the field.
click 'convert video'.
It converts the audio to mp3. then you click 'download', and choose whether you want to 'open'', save, or save as. I always choose 'save as',....so I can choose where it goes. I put it in my 'music'.
I have hundreds of pieces of music saved this way. All perfect, high definition audio.
Good luck.
Jenny