There is a therapy recommended sometimes, called inversion therapy, which technically does what you’ve described, using a piece of equipment. I don’t know how popular this is, or whether anyone on this site has tried it but I did wake up once with my head hanging off over the edge of the bed and I felt good too – though I couldn’t repeat this process, so obviously ‘angle and position’ must play a part in it.
I can see how it would work (on those who don’t have CCI or compromised circulation), as gravity does play it’s part in our condition. I think it could temporarily partially ‘unbung’ any cerebellar tonsil that is blocking ‘cerebrospinal fluid (CSF) flow’ between the head and the spine, which contributes to the back of head (occipital) headache we have, plus the neckache and probably shoulder ache. This would allow freedom of flow of the CSF, which would temporarily lesson any intracranial pressure, thus probably improving blood perfusion to the brain area.
For those with Craniocervical Instability though, you could risk further stretching the brainstem, so for that reason (plus the circulatory issues) I wouldn’t try it.