Despite incredibly effective tools to prevent HPV infection and treat precancerous lesions, the scale-up of existing interventions in most low and middle-income countries has been slow, leaving a residual burden of invasive cervical cancer that will persist for decades. An HPV therapeutic vaccine may overcome some of the scalability and infrastructure challenges of traditional screening and treatment programs, though its potential public health value depends upon its characteristics, delivery strategy, and the underlying natural history on which it would act. This analysis uses HPVsim, an open-access agent-based simulation framework, to evaluate the impact of a potential HPV therapeutic vaccine with varying scale-up of existing preventive interventions. To illustrate the sensitivity of results to natural history assumptions, we calibrate two models reflecting uncertainty in the natural history of HPV infection and cervical disease. We find that an HPV therapeutic vaccine may avert 7% to 30% of cervical cancers over 30 years and 25% to 60% of cervical cancers over 70 years. The size of the impact is sensitive to rates of background intervention scale-up, the characteristics of the vaccine, including ability to establish long-lasting immune memory, and the underlying natural history assumptions. Even with background intervention scale-up reaching WHO cervical cancer elimination target levels, an HPV therapeutic vaccine might have efficiency comparable to many other widely administered vaccines such as against MenA, rotavirus, and PCV. This work highlights the importance of the underlying natural history assumptions in mathematical models and the need to explicitly account for parametric uncertainty.