Get classification score of hypothetical detection box
With tensorflow you cannot do that. What you are saying is almost like a region proposal and rest of the pipeline on which different platforms like tensorflow, yolo are built to arrive at object detection. You are proposing to a built a different platform by asking what you are asking.
Is there anyway to assert the presence of a detection box in an image and obtain the classification score of said hypothetical box? 
I am working with a tensorflow object detection graph and want to refine it's accuracy with a little trickery; by making the claim that there are more (N) objects in a given image than it is detecting, asserting there are image objects in multiple areas in the image, and evaluating each hypothetical image object based on it's classification score between 0 and 1.
In other words:
I want to say "Hey, TensorFlow, I think there is an image object with rectangular coordinates (x1, y1), (x2, y2) in this image. What would the classification score of a hypothetical detection box defined by that rectangle be?" Is this possible?