No you don't.
At Fox we provide super-effective and safe sessions. This is partly due to the way we design each session around heartrate principles. This means that with or without a heartrate strap, you'll be able to pace yourself as you'll be able to keep an eye on exactly what's coming next. Your instructor will let you know how each challenge should feel if you're not wearing a heartrate strap and this will give you a good idea of how hard a challenge each section should be.
The structure of each session is designed around physiological and psychological principles, to help you enjoy the session, and achieve greater results than with other classes (even other cycling classes). Therefore you will achieve most of the benefits with or without a heartrate strap.
Having said that, the vast majority of our riders do wear a heartrate strap because they enjoy the extra motivation and fun that comes with it. It is also a safer way to exercise as you are learning how your body responds to activity and you are able to stay in charge of how hard (or not) you push yourself.