Question regarding downloaded music quality and streaming

Hello everyone,

as the title says, i have a question about Apple Music and its downloadable music.

My question for you: if one downloads a song with a certain quality (let’s say High Quality), will that song play in the quality it was downloaded, even if there is internet connection available and internet streamed songs are set to play in another (say Lossless) quality?

I know it’s a random question but i couldn’t find any article explaining this.

Feel free to ask me anything to better understand what i am trying to understand.

Thank you!