No, you can complete every workout with, or without a vest. If you plan to wear a vest for Murph, a vest is recommended for the program, but not required.
How long is the program?
This is a 6 week program. Ideally you finish week 6 the weekend prior to Memorial Day weekend. However, you can start at anytime. Even 1-2 prep workouts are better than 0.
What if there is less than 6 weeks until Murph?
You can still use the program! Just start on week 2, and do as many weeks as you have time for. Even just a few workouts will prepare you much more than 0 training.