Yes, most communists and especially Marxists believe communism must necessarily be fully democratic. It’s certainly true though that there is much debate about what types of democratic structures to use. Although most communists would probably agree that it would require a lot of trial and error to find an ideal system.
That said, communists generally seek to disenfranchise owners of capital from the decision making process up until the point they no longer exist as a class. Therefore in the transition to communism, full democracy may not be realized. This is the given reason for why Marxist Leninist countries generally suppress opposition parties but may allow for political affinity organizations around identity groups that suffer under capitalism, ie worker, youth, women’s organizations, etc.