Actually, if you looked at Bojak's Undercover Kojak's OFA listing it has all his health tested offspring. If the dog that is behind your dog isn't in that list then it wasn't tested.
You only have to type in every name if only 1 or 2 dogs were ever tested. In the case of a petstore dog, your right you will probably have to type in every name and you will probably find only a couple that were ever tested because puppymills who supply petstores don't test.
I know some of the dogs that have been used for breeding for petstore dogs. Do you have the names of the sire and dam of your dog and the breeder's name, city and state? Would they happen to go back to Tankersley's, WL's, and/or Reedgate's kennels?
I did a reverse pedigree on Omar's They Call Me Junior and one can follow it to the Misty Mountain kennel. Some of their Bs went to rescue and the remainder went to other breeders, Tankersley, Reed, Choate-all commercial breeders. I saw some of these dogs at the dog auctions.
Then your puppy cannot be shown in conformation shows.
In order to show in conformation, your dog must AKC registered. APRI is a registry used by breeders who did not want to follow AKC's rules. Either breeding dogs that were designated non-breeding by the breeder with limited registration or refusing to do DNA profiles on frequently used sires to prove paternity.