Yes when sleeping with a pillow your head should be on the pillow along with your shoulders and neck.
The pillow should follow the natural curves of your head, shoulders and neck for proper support.
So if you're sleeping without your shoulders on the pillow then you could suffer from neck or shoulder pain and are not sleeping properly.
So always if possible rest your shoulders on the pillow when you're sleeping because when you sleep with your shoulders on the pillow you'll prevent shoulder pain and neck pain and be supporting your shoulders properly.
I've slept without my shoulders on the pillow before and I had shoulder pain and neck pain as a result.
After sleeping with my shoulders on the pillow the neck and shoulder pain went away.