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My answer is yes provided that the line is anchored, for example if one of its ends is in the center of the image. The solution is using NN for reverse transformation. The net is a universal function. You can remember discrete associations input-output, then use it in reverse direction. In this case, direct transformation is rotation around the centre. Here, the simplest 2-layered perceptron was used. An input image is at the left. The central matrix represents NN output similarly to Hough transform. The angle of rotation (clockwise) is X and line length is Y (downwards).

Of course, this method has a lot of conditions. I am going to post a more detailed report later.