There are two types of project maturity models. One is the "stair step" where organizations try to put things in place to reach the next level. Kerzner's PMMM is an example of this. On the other hand, models like PMI's OPM3 look at maturity as continuous improvement and measure maturity on multiple factors -- there is no specific goal except to continuously improve along each dimension of the model.
Having a PMO is no guarantee of a certain maturity level. Some PMOs are incorrectly created and managed, so like any other corporate change, may or may not contribute to maturity.
I'm not aware of any survey indicating the maturity of organizations with a PMO, however if the goal of a PMO is to put in place repeatable processes, organizations with a PMO will have a good chance of reaching a level 3 and beyond in the PMMM model.