Yes, you will need to complete your 35 hours (including passing the final exam and receiving your completion certificate) before submitting your application.
That said, once you have completed the PrepCast lessons you should go ahead and take the 25-question final exam and get your completion certificate. There's no reason to take additional practice exams or do additional study if you're worried about time - if you don't pass the first time, you can take it again as many times as needed, and once you pass you'll still have access to the PrepCast resources and can continue your study plan as desired. The final exam is not difficult if you have been following along with the lessons, and there's no penalty if you fail it, so I strongly recommend you take it as soon as you can.