It depends but generally, no. Furthermore, they are not even tested until they are loaded up and shipped off to holding facilities... across many southern states like LA, AL, GA and the like... and even some mid-western states.
The most depressing part is that texting/vaccinating everyone coming through isn't even CPB's oversight or failing. They are not capable of handling such a large influx of humanity... not even the fraction that they are able to interdict... to say nothing of whatever percentage is getting through or dying along the way. But all of this was known from the beginning... and why repealing Trump's border policy was not only a mistake but pure, unbridled idiocy... perhaps even malice. Even with Kamala and Biden actually coming out and telling immigrants "Do not come", their actions are speaking many times louder than their words to those that view this as their chance to game the system.