That only works for desktop use, on mobile it's slightly more complicated. With Premium you can use the official app with your screen locked or the video minimised, and you can download videos for offline viewing. Some of those are available with third-party apps for Android.
However, a weird limitation i noticed recently with YouTube Premium - while traveling i had a local sim card, and while using it for data ( even when on wifi), YouTube earned me some Premium features won't work and i might see ads, and i couldn't watch videos with the screen locked/minimised. When i switch data to my regular card, in roaming ( again, regardless of wifi), both of those work.
However, a weird limitation i noticed recently with YouTube Premium - while traveling i had a local sim card, and while using it for data ( even when on wifi), YouTube earned me some Premium features won't work and i might see ads, and i couldn't watch videos with the screen locked/minimised. When i switch data to my regular card, in roaming ( again, regardless of wifi), both of those work.