Q: Is it possible for music downloaded from Apple Music to be synced to iTunes Music Library?

Ofcourse! It's fairly simple but I can only speak for myself. How it's done, in my opinion, differs on the hardware (computer) you're using.

Here are two links which provide step-by-step instructions on how it's done! Hope it helps!

For Macintosh (Apple) computers:

http://www.imobie.com/support/transfer-music-from-iphone-to-macbook-pro.htm

For Windows (PC) computers:

https://m.youtube.com/watch?v=pzRVHtJLzoI

If your iPhone 6 and the iTunes Library on your computer are signed in with the same Apple ID any music you add to your Library on your iPhone (or your computer) should automatically show up in the My Music section of the other device/computer. However, if you download music from Apple Music to your iPhone for offline listening, while they will still show up in your library in iTunes, they will not automatically download to the computer.

Also, you must have Apple Music AND iCloud Music Library turned ON on both your iPhone and iTunes and both signed in with the same Apple ID.