This is a complex question, and it is unlikely to have a definitive answer. However, if we look at the standard definition of democracy, we would have to say that an unelected Supreme Court is not truly democratic.
The concept of democracy is that of popular rule. In a democracy, it is the common people who are able to make decisions when it comes to politics and government. They do so by electing their leaders. If the people of a country cannot directly influence the decisions of the Supreme Court, nor can they elect the people who do, we would have to say that the Supreme Court is undemocratic.
