Can spinal stenosis injure other body parts?

Indirectly: Spinal stenosis can only directly injure the nerves running past the narrowed area in the spine. If the nerves are badly damaged enough! there can be problems in the parts of the body that they control.

Not usually but: Not in the lumbar spine except in severe, long standing cases or in people with an underlying neuropathy, there can be muscle wasting or atrophy or even permanent nerve changes leading to continued, numbness, tingling &/or weakness. In the neck, it can also injure the spinal cord permanently and this can happen in the thoracic or chest level as well.