The ones given false Paleblood didn't know that they were getting it, no. For most part it has been a matter of the church contaminating isolated food and water sources to infect people with the disease, but they also straightforwardly injected anyone signing up for blood treatment around the time of the start of the RP with it.
People also weren't selected for receiving false Paleblood as much as they just spread it at random. It's an experiment as much as it is an attempt to actually produce immortal Hunters to cull the scourge of beasts; there has never been false Paleblood Hunters before, and the church wants as large a sample size as possible so they can tell how well it works.