If you knew the Mashiach, and he was aware he was The Anointed One, would you spread the news?

Of course! Yishayahu/Isaiah (40, 9) actually relates to your question: "Upon a lofty mountain ascend, O courier (=messenger) of Zion, raise your voice with strength, O courier of Jerusalem; raise [your voice], fear not; say to the cities of Judah, "Behold your God!" As we've written many times here, the main issue is not the person: Mr. Messiah, but the time period, the "Messianic Era", of which he arrives only at the end (Megilla 17b). Accordingly, although many, if not most, of that era's prophecies have already & are being fulfilled over the recent century (e.g. the gathering of the exiles back to Israel, the flourishing of the Land of Israel and her economy, the Holocaust, the wars of Israel, the technological revolution etc.), still many people, including believing Jews and even some rabbis, don't realize what's taking place and need to be alerted (that's why the messenger is fearful- "how is it I see what many others don't see?!)! This alert is not only necessary, but very beneficial in that it motivates us to return to Israel and Torah.