Yes, a person can always have an HIV voluntary testing, but the most probable result would be nonreactive or negative to HIV. Usually the virus stabilizes in the body 2-3 days after exposure. If the virus is already stabilized,you can be tested with an HIV antigen test which directly identifies the presence of HIV inside the body, but then it costs higher than the usual HIV test.
On the other hand, if you are going to use HIV antibody test, you must wait for at least 3 months before you undergo HIV test because the body can only generate antibodies against HIV 2-3 months after the exposure. Because in this test, you are detecting the antibodies made by the body and not the antigen or the virus itself. If the test result is nonreactive (negative), you can repeat the test 6 months after, then after a year.
Though our body can make antibodies against HIV, the virus can replicate and reproduce hundredths to million in a day, and most probably,HIV mutation has already been severed.