I never heard that an eye exam in the morning will make difference from in the afternoon. But I ever heard that farsighted people have a stronger prescription in the morning than in the afternoon. However, you should check with your doctor.
The best time of the day for an eye examination is dependent upon when you are most alert. If you are a morning person, then an AM appointment would provide better results. If you are scheduling an examination at the end of a 14 hour day, you may be very tired and your responses during the refraction may be difficult. Always consider the weekends for an appointment with your optometrist.