Much like with a typical hiring process, you will only need to provide references if you have been contacted by Teach Away or a school in regards to your application.
Having references attached to your profile in advance certainly doesn't hurt. Sometimes, getting in touch with a referee can take longer than you expect. If you already have some contacts you'd like to reach out to then send them a reference request at your convenience. We recommend giving them a heads up about your intentions to teach abroad or online and any other information that will help them provide an outstanding reference.
Schools are also able to review your references after you have applied for a job and it may be a determining factor in whether they decide to reach out to you in regards to an interview. But not having references already part of your profile does not impact your chances of obtaining a job offer.