Within a constitutional framework in which Shari’ah is enshrined as the supreme law of the land, and the with appropriate legislative powers of the government limited within these parameters; there is no reason why democratic mechanisms would be objectionable in Islam.
Furthermore, even without such a framework, there should be no hesitation to participate in a government that is not officially committed to Shari’ah, if it is possible to achieve good for the society through your participation.
As Rasulullah ï·º told us, when our government introduces things we do not recognize, and becomes oppressive, as long as we do not approve of these things, we will remain innocent of them; and I do not know of a better way to express your disapproval of things you disagree with than by working on a practical level to change them.