No, caffeine is not necessary. It does not shift you faster, but it helps you fight fatigue. It might make it slightly harder for you to follow the plan without it. Exercising will help you stay energised. You could also consider using caffeine in tablet form.
No matter what, please follow the "Avoid caffeine" advice. Caffeine is also to be found in cola, chocolate, tea, etc. And caffeine can worsen the quality of your sleep if consumed too close to bedtime.