Absolutely, uniquiviquly, NO you can not assume that if you have normal blood pressure and pulse range that you are otherwise healthy.
Periodic physical exams are recommend for all persons, even if they seem otherwise healthy (this provides a good guide to determine frequencies).
But there are some clear exceptions to this. AIDS is caused by HIV infection, and can be diagnosed without abnormalities in pulse or blood pressure. More pressingly, HIV infected patients often live several years with little to no symptoms what so ever (before the development of AIDS, during the clinical latency period). Further, HIV treatment has the best outcomes if it is begun prior to the development of AIDS.
If you believe that you have been exposed to HIV, (a good summary of transmission information for the public can be found from the CDC) you need to be screened for HIV. If you are unsure if you should be screened, then you should consult with your primary care physician (which if you don't have one, it is best to try and obtain one). World wide, it can be difficult to obtain primary care, and several agencies, NGOs, and charities are trying to fill that gap.
Medical conditions missed by normal vitals are not limited to infectious diseases. Anemia is just an easy, common, example of a problem that can present with normal heart rate (HR) and blood pressure (BP) (and temp/respiratory rate).
The short answer to your question: HR and BP are NOT assurances of good health, just a good place to begin looking for problems.