iTunes ain't synching any music from iTunes to your iPhone anymore. The phone is synching all music directly from the 'My Music' section of your iCloud Music Library. If there are songs in your local iTunes library that aren't available in the Apple's online music catalogue, then iTunes uploads them. (Though if new songs are available locally on your Mac or PC, eg, ripped from a CD, it might copy them directly from the computer instead of downloading them from Apple servers to your phone.)
Unchecked songs (in your iTunes library) are considered to be part of 'My Music' for the purposes of Apple Music but for iOS devices are labelled as non-downloaded songs. Thus, if you set your phone to only show content available offline, it will not show the not-downloaded songs, which in this case means it will not show songs that are unchecked in your library. You find that setting in the 'My Music' section within 'Music' on the phone if you open the dropdown menu that let's you select between viewing artists, albums, songs, etc. (I just had to hunt for that setting for a few minutes as I looked for it in some sort of general settings area (either in the Settings App > Music or under the Account settings)).
