Couple of points:
1. On a precision approach the DA is at the MAP, so no, you don't normally climb out before the MAP on a precision approach. However, if you did do a missed approach prior to the DA then you would climb out straight away.
2. You say it is common to be out of tracking tolerance. No, it is not common. What is common, is to track down the middle of the approach and either get visual and land or not get visual and go around. I have never been, nor seen anyone fly, out of tolerance outside of a simulator session.