Most installers only wrap the front of the mirrors due to difficulty and usually the "inside" part of the mirror doesn't get rock chipped. Some installers can wrap the entire mirror, but best believe you're going to be paying for that extra work and time.
Yes, if the mirrors are dirty, you'll see dirt collect on the edge. Some brands are much clearer than others, so if you get those + keep your mirrors clean, the line will be barely noticeable.