No, this is false.
A Testosterone cycle will cause HPTA SHUTDOWN so that when the exogenous hormones exit your system, your endogenous testosterone levels are extremely low. During this time, most users will run a Post Cycle Therapy in an attempt to restore testosterone, which is often times very successful.
Natural Testosterone boosters will NOT cause HPTA shutdown, as they will NOT increase your testosterone levels beyond the normal physiological range. They will simply elevate your NATRUAL testosterone enough to create the optimal hormonal enviroment for natural growth.