Yes, of course.
Democracy without Permanent Unchangeable Values is only ruling by majority on minority, and it per se neither guarantees justice nor provides equity.
Human is not perfect, he has no inborn conscience and his emotion and personal attitudes intentionally or unintentionally may affect his decisions. so man-made rules are not always just. Therefore, we need a source that can give us perfect criterion of basic right and wrongs. God as His Law of Guidance has done so, and His Manual for us is the Quran. It can give us those immutable basic laws we need in our collective & social life.
People considering the basics can provide by-laws by mutual consultation and democracy.
Some noteworthy verses of the Quran on the subject:
6:116 (People will confront you with what the majority is doing, as proof of right and wrong.) Now if you pay heed to, or get intimidated by majority of those who live on earth, they will lead you astray from God’s way. Most of the people follow nothing but conjecture and they only live by guesswork.
2:11 When it is said to them, “Do not cause disruption in the land”, they assert, “We are but reformers, setting things right.”
2:12 Nay, it is they who are the disrupters. But they fail to use reason. [They bring forth a common argument that they are acting in good faith and in accordance with their ‘conscience’. But conscience is only the "internalized society", a mental reflection of the values prevalent in a given environment. Therefore, it can never be a substitute for Divine Revelation (Wahi). 3:20, 5:79, 9:67, 24:21]
42:38 They respond to their Lord by establishing Salaat, and conduct their affairs by mutual consultation, and they keep open for the welfare of others what We have given them. [Establishing Salaat = Establishing the System where following of the Divine Commands is facilitated. Nafaq = Open-ended tunnel = No hoarding]