Could spinal stenosis affect the brain?

Not typically. Spinal stenosis is a narrowing or pinching if the nerve canal, it can usually affect things spine related, but not really brain related.
No. Spinal stenosis is a diagnosis related to the spinal canal and the neural elements found within when there is too narrow a canal causing pressure on these neural structures and the brain is not one of those structures found outside its own bony cover, the skull's cranium.