No, the Bulletproof Trust is not drafted to be this type of trust; however, one can customize the trust indenture to specificy these requirements.
When a grantor is paid from the trust it created, this is considered a Grantor Retained Annuity Trust (GRAT) and is a type of irrevocable trust that allows the grantor to draw income from the trust. Assets are transferred to the trust and the grantor receives annuity payments for a set period of time. After that, any remaining assets revert to the trust beneficiaries.