But the thing is that democracy in the Islamic world seems to invariably take a populist form that doesn't vent off the perception of victimization and scape goating, it just makes it even more legitimate. Heck, democracy in the UK and Spain doesn't seem to stop the rise of Islamic terrorism.
I believe the root cause of Islamic extremism is that Islamic culture (which includes but is not the same as Islam as a religion) cannot create stable states which can be economically, technologically, and socially competitive in the 21st century. But, to the extremists and those sympathetic to them, admitting this would be admitting that their religion is flawed. So, instead of blaming the real causes of their poverty, weakness, and instability, they seek scapegoats. And the West is it.
To me this means that Islamic democracies, assuming they retain the dysfunctional elements of Islamic culture, are still going to be uncompetitive, weak, and unstable. So they're still going to seek scapegoats. If anything, a democracy will be less effective than dictators like Musharaff, Mubarak, and the Sauds at clamping down on this.
I believe promoting democracy is a good thing in itself. I think it will have no effect on Islamic extremism.