This is possible, but not necessary. The way houses were built was with wood for truss support, then a layer of reeds on top of the trusses and clay on top of the reeds. They allowed nothing to stop them. Faith works - The men expended great effort to help their friend. Faith persists - They didn't let personal inconvenience stop them.
Faith succeeds - Their faith was rewarded.
The man was healed. Luke is stressing that Jesus is a God empowered man. He simply makes a statement. The authority and power of Jesus' word is demonstrated. I don't think this necessarily means that the man's paralysis resulted from personal sin.