Depends on the Boss.
Competence abounds where I work, and shit work is noticed really quick. I've landed two successful (medium) projects in the last two years and am working on a third (smaller). In the echelon-or-two above me there are two brilliant project directors who Get It Done (although one, to be fair, does a very large percentage of the code- even re-writes programmers work).
But, I did watch a project 'Software Proj. Director' (really a glorified programmer), not in my shop, nearly torpedo one multi-million project... A little incompetence at the right level goes a long way, I will grant you that point.
Davin L.