How likely is it that PhD application is not reviewed by professors if TOEFL minimum isn't met?
I do not know about US schools, but for my UK university the IELTS requirements are non-negotiable. Most of the time we see this right away. Sometimes we screw up and read and evaluate the entire application before noticing. In all cases the student is not offered a place. Other UK universities, especially ones that struggle to fill their spots, sometimes will argue with the administration that an exception should be made. From my understanding, they almost always lose.