Islam can work democracy - but not radical Islam. There are forces within countries that are predominately Muslim that will work with ziel against the introduction of democracy. But I think the real question is whether Islam is compatible with free choice - freedom. Yes, if Islam does not depend of sharia law for its survival.
Islam is comparable to democracy. Was created 1400 years ago in Middle east. God chose Muhammad peace be upon to spread the world of Islam. Islam in English would mean submissive to one God. Islam has been criticized because those who claim to follow Islam use Islam in the wrong negative way. If Muslims and non-muslims were truly educated about Islam they would know Islam itself is democracy because the religion itself meets people's needs such as economic, spiritual, and education needs.
No, Islam is not compatible with democracy, because Islam, is, by its nature, a rigid set of rules to which all people must adhere. We are told to tolerate Islam, but Islam does not tolerate any other system of belief. The rulers of Islam rule with an iron fist. Democracy cannot survive in an Islamist state, because Islam does not allow people to make their own choices.