There’s a small port on the east side of Taiwan which could be used to supply some of the bare necessities. I don’t know if USA would fully enter a war but I do think they might do freedom of navigation exercises east of the island. Would China dear hit a US military vessel with missiles and escalate the conflict. I don’t think so.
There is no part of TW that is not within PRC land base munition range, every inch can be hit within 7 minutes. Of course PRC would hit US ships in blockade scenario which is by definition war. If USN doesn't blockade, then FONAP does nothing, anything supply ship to west TW would be trivially sunk, NVM legally any ship during PRC TW blockade scenario is running PRC blockade (read: entering sovereign One China waters) and can be treated as hostile. US either tries to blockade (goto war with PRC who will run blockade / test US resolve), and if turns hot, risk its westpac / global replenishment chains (including CENTCOM/CONUS) being blown up, or CONUS hits. Just hitting USN replenishment ships, which are exquisitely vulnerable (has to spend hours in port) means USN becomes single deployment assets, i.e CSG in high tempo operations will exhaust fuel (escorts), munitions in days. USN expeditionary model simply isn't viable vs peer who can cripple US logistics tail within ~10000km radius of PRC. Or US does functionally nothing, i.e. FONAP in TW blockade scenario is theatrics.