Theoretically, yes... usually the new variety is started as a 'project'... once it is well into development, you'll need several interested parties to help your project achieve the desired results...
Susan knows the exact details and steps towards acceptance, but I do believe the hardest issues are that you (or at least your helpers) need to be APA members for 5 years and breeding the project 'true' for 5 years and there has to be at least 5 APA members that are the involved willing to promote and show said variety... and then it needs to be petitioned to the APA for acceptance which cost $300 for that alone...
There's more to it, but Susan knows those parts much better than me... it involves meets and shows, placing of the birds of that variety, etc...
That help answer your question?