What is quiet? What is awkward?
Being quiet is not inherently a bad thing. There's nothing wrong with being a person of few words. And often times, there will be situations where a quiet person will really love to talk and share their opinion. We humans are social by nature, and even the quietest of people can hold a conversation. As long as a person is capable of communicating their needs, wants, opinions, etc. when it matters most in the relationship, I don't see why it couldn't work.
So, there are many ways you can be awkward. I'm going to guess that you mean awkward in the sense of having difficulty saying the right thing in social situations, difficulty translating thoughts into coherent words under pressure, feelings of discomfort in social situations, or having uncommon mannerisms. A quiet person might actually be the best with an awkward person because they would take the time to see past all that (presumably). Awkward people all have their comfort zones, and it's just a matter of these two people being comfortable together. Obviously, they would have to get to know each other and be in the right settings for this to happen.