If ICAO is part of the United Nations, you'll need to get China's OK, or your petition is going nowhere. China is a member of the UN Security Council and has a veto. I don't suppose that China would approve Taiwan's petition to join unless it's under the name "Chinese Taipei" or, more likely, "China's Province of Taiwan." Perhaps the first term would be tolerable (barely) to the Taiwanese, but I suspect that the second would not, so I don't see this as a realistic exercise. But good luck with it anyway.
As for the US Congress passing resolution to support Taiwan's membership in ICAO, that would be about as effective in moving China's position as a petition from my dentist or the local betel nut vendor.