Very low. Lavender orps may have better chances than polish, since they haven't been around as long and most hatcheries haven't had them for as long so they can't have messed them up as much as they have, say, buffs, lol.
But in general a bird from a hatchery is never going to be competitive against birds from a show breeder that is actually focusing on just a couple breeds and choosing breeding stock based on the standard. Even when you're breeding like that, only one out of ten birds is usually good enough to breed from, and then maybe one of ten of THOSE is a good show prospect.
But for a fair, you might be fine IF it's not APA/ABA sanctioned. Fairs are often not judged by actual sanctioned APA and ABA judges, and people entering them might also just be entering hatchery birds, unlike shows sanctioned by the APA/ABA where APA/ABA members are competing, there are APA/ABA judges, and the winners gets points.