You are using sent so the dog will at least have an assosiation with that sent, but he/she will also hunt other birds. Mine will point rens, Cardinals, chase tweeties. But to answer your question, can the dog be trained to hunt only one type bird? I don't know, Mine had been on quail, Chuckar, Pheasant and waterfowl already. The more experianced folks will have to answer that. maybe ask in the hunting or sporting dog forum.
I agree. Bottled scent is a good starter, then find roadkill birds or go to someone locally that raises them, buy a couple and (with our labs we have done this) clip the wings and plant them. The problem with "tame" birds is that they don't run that much usually. Nothing can take the place of actual in the field experience. Get the dog out as much as possible, and it will be much better. Didn't notice where you are from, but the best thing that has ever happened to my dog, and several other MN dogs is a couple trips to SD. Maybe nowhere else to get on that many birds every day.
And I would LOVE to see anyones dog who claims that it only hunts one species of bird. Or better yet, I know a couple guys that claim their dog will only run roosters. Won't even sniff at a hen.