yes. x-rays show bones, MRI soft tissue very well.
Although the diagnosis of instability is made many times on history and physical exam alone, MRI/arthrogram can show a labral tear or other pathology that could be lending the shoulder to instability. However if you just have a sloppy capsule that is causing the instability, many times the MRI/arthrogram may appear normal, or have a large amount of redundancy of the inferior capsule seen sometimes on the MRI/arthrogram.