In short
The fact that the paralytic immediately rose and went home reveals his faith in Jesus’ power to heal him, both physically and spiritually, since he obeyed Jesus, and glorified God on the way (Luke 5:25).
Yes, the paralytic sincerely believed in the power of Jesus’ words when he commanded him to rise and go home. Miraculously, he was also immediately able to do just that. He thereby acted in faith, having been healed both bodily and spiritually. The Gospel of Luke also mentions that he glorified God on the way home (Luke 5:25).1
7 And he rose and went home.