LOL. Try telling someone using AM and those services that they are separate. If I purchase a song from the iTunes store, where does it show up? In the Apple Music library. If I continue to subscribe to Match, there is not some separate application, it's all unified. It sounds like you don't really understand what Apple Music is. You still think it's a separate app. Apple Music is the streaming service that is integrated into iTunes. You can use iTunes without using Apple Music, but you can't use Apple Music without iTunes.
No, your song does not show up in the "Apple Music" library, it shows up in your library, in iTunes and in the music app on your phone. The song was likely already IN the Apple Music library (unless it's by Prince or one of the other artists who have not allowed their music in the service).
Match is a separate service, also not a part of AM. Both Match and AM leverage the iCloud Music Library. When you use Match, songs you upload/sync become part of the iCloud Music Library. AM can see what you've added to iCML and makes those songs available for streaming. This is components working hand-in-hand, not one being swallowed by the other.
It seems you're thinking about it backwards. If you turn off Apple Music, everything you still have access to is NOT part of Apple Music. Your library, the iTunes store, Match, etc., are all still available. So yes, you can use iTunes without using AM, because iTunes is not part of AM.
If you do a search you'll find a very long thread that explains how Match is a separate service that integrates with AM and how it affects what files you'll see in the iCloud Music Library. As you seem to be a Match subscriber, you might want to check that out, as the way all these different components and services come together may directly affect you down the line.