Yes spondylolysis can eventually cause paralysis
If the spondylolysis is left untreated and allowed to progress it can eventually lead to and cause paralysis especially in the legs.
If you have spondylolysis you need to seek medical attention and get treatment for the spondylolysis because it can cause permanent damage.
You can also experience weakness in the legs when spondylolysis is left untreated and when you do get weakness in the legs as a result of spondylolysis then it's a sign that you're likely about to become paralyzed.
Especially if you have suffered nerve damage then your risk of getting paralyzed from spondylolysis will increase.