Frederic L. Pryor has conducted a study that seems to show that "in all but the poorest countries, Islam is associated with fewer political rights." The abstract of the study can be found at the Middle East Quarterly.
Note that Pryor does not say that Islam causes a lack of political rights, but is associated with it. This makes it a chicken-or-egg question: is there a lack of political rights in these countries because of Islam, or does Islam find a foothold in such nations because of that nation's geography and history?
I remain unconvinced that Islam and democracy are incompatible, and Pryor even points to several democratic nations that are both Muslim and poor, such as Bangladesh and Mali. For those of you who want to argue the incompatibtility of Islam and democracy, I am not sure this study helps you much.