On the end of an end mill, no it will not leave a mirror finish most of the time. The cutting speed, no matter what the spindle speed, is zero at the center of the cutter, and that always is a hindrance. I don't believe a face mill will leave an acceptable finish on the shoulder. Of course, you're welcome to try it, but my recommendation would to cut up to the shoulder with a face mill, then use an end mill to clean up the shoulder. I really think you will be disappointed with the shoulder finish. That's not really what they are made for.
If you can cut the bottom of the recess, or slot, or whatever feature it is, then flip the part 90° so that you are actually facing the shoulder (the reason they are called face mills), just kissing the previously cut surface, you might get by. Then your obstacle will be chip control as you get close to the finished surface.