TBH I don't know for sure.
I do know that the first tests made available tested for the presence of antibodies to the HIV rather than the virus particles themselves.
Now they might be testing for the virus itself, I don't know. But even if that is the case there will be a lag period between first being infected , and producing enough virus particles to show positive from the test (the test will have a minimim sensitivity level, I would assume). There is a tiny, but nevertheless possible risk of that blood infecting someone.