I think it should be possible do automate this task. The steps you need to take is to first create a world file for each image. The world file is usually a text file with the same name as the image file, but a different extension (e.g. tfw for tif). The world file contains the coordinates of one of the corners, the rotation of the image, and the scale in the x and y directions. These numbers should be easy to calculate given that you have all for corners of you imaga.
When you have the world file you can add it to the map and it should end up in the correct spot, if they are in the same projection, but the projection information for the image is still missing. To add that just use the ArcToolbox tool Define projection.