Depends:
I suppose if one is young, or even middle aged and healthy, then sleeping with a pillow may well strengthen the muscles of the back and neck.
However, if you are 60 + years of age other factors come into play which may suggest that sleeping with no pillows is a BAD thing.
Wear and tear of the cervical spine may lead to pain and indeed reduced blood supply to the brain if one sleeps flat.
The more important consideration for the "elderly" would be a compromise of the heart leading to heart failure, particularly if one had diabetes , high blood pressure or a degree of heart incompetence.
So YES and NO.