How likely is it that PhD application is not reviewed by professors if TOEFL minimum isn't met? I am applying to doctoral programs and I have a worry about the application.

Since I found that my TOEFL score does not meet the minimal requirement set by a school that I am applying to, I am wondering if it is likely for me to be screened out before my whole application is reviewed by the professors?
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.