The patella is a sesamoid bone that typically doesn't completely from and ossify until ~3-6 years of age (e.g., Source). My long-standing understanding (supported by a claim in Saladin's college A&P textbook1 sitting on my shelf) was that sesamoid bones form "in response to stress."
Well, I had a student in my anatomy class this morning ask me the titular question about people born with leg paralyses or other congenital issues preventing them form walking. To their point, if such congenitally paralyzed people never walk and therefore never place stress on the knee via the quad tendon, would they ever form a sesamoid bone (i.e., the patella) in the knee?
I've done some digging and found evidence of "nail patella syndrome" (e.g., here) which results in people not forming a complete patella. However, I was unable to quickly narrow down any sources discussing lack of patellar growth due to congenital leg paralysis.
1. Saladin, K. S. 2015. Anatomy & Physiology: The Unity of form and function. 7th edition. McGrawHill, Education, New York, NY