I've had a dominant reliever and a solid closer both come out of rounds 15-20 in drafts before. My reliever was the highest rated MR in the game and his career ERA was right around 2.00 in his 4 years in the majors. My closer averaged about 30-35 saves a year and always seemed to have a sub-3 ERA minus a few years. I don't remember exactly what picks I drafted them with, but I remember seeing that I'd taken them in the 16th or 17th round of each of their drafts. Both started out with very low overall and potential ratings, but I drafted them based on their good work ethic and intelligence.
It took them longer to develop and I don't think either one made it to the big leagues before their age 25 season, but I couldn't tell you the exact ages or stats they had in the minors. That save file was on my old Mac that has since died.