We are not told whether or not Aeneas was a believer. Possibly he was a man who lay by the side of the road, begging alms (see Acts 3:1–10). The fact that Peter goes to visit the believers in Lydda and that his name is explicitly mentioned suggests that he was one of their company (a believer).1
33 There he found a man named Aeneas, bedridden for eight years, who was paralyzed.