As a convert, I clearly do not know any Hebrew. Although I prefer to pray in it with my Artscroll Transliterated siddur because that is how I feel closest to G-d. However that begs the question, am I required to learn Hebrew to daven in Hebrew since I do not understand it?

You definitely should learn Hebrew for many reasons. It's our national language, something especially important for converts to feel and be totally part of our nation. It's spoken and used for prayer by all Jewish communities from Yemen until America and obviously Israel, where it's our spoken language. Whatever synagogue you visit in any country, you will and should feel at home and be able to pray with them. Contrarily, the Reform movement began to pray in the local vernacular as part of their plan to assimilate, and lose their Jewish identity. Hebrew is the language of the Bible and prayerbook, and in order to understand them properly and to analyze and fully enjoy their vast wisdom, it should be learned in the original. Hebrew and her letters have an inherent holiness and reveal Godliness and ideals even in mundane and secular topics. It's God's language and in which He spoke to the prophets, and with which He created the world ("And God said: Let there be…). In addition, every language expresses a life-philosophy, how much more so, God's language of Hebrew.