Can a herniated disk at l5-s1 protruding centrally into the thecal sac affect a person's bowel movements?

Yes: Be careful. Qauda equine syndrome, a rare disorder affecting the bundle of nerve roots (cauda equina) at the lower (lumbar) end of the spinal cord, is a surgical emergency. If patients with cauda equina syndrome do not get fast treatment to relieve the pressure, it can result in permanent paralysis, impaired bladder and/or bowel control, loss of sexual sensation, and other problems.

Yes it occurs in 1% : Of all herniated discs and it is called a cauda equina syndrome and it is a true surgical emergency with the best outcome with surgery done within the first 24 hours of symptoms with decreasing chances of recovery over time. It usually would involve both bowel & bladder control with numbness & tingling in those regions.