No formal alliance, but in reality, if you look up the proportion of Taiwanese-made chips used by the US military in... everything - aircraft, missiles ,tanks, planes, everything - invading Taiwan would probably cripple the US military's production capabilities so it's probably kicking off a proper war with USA.
It would be a headache but it wouldn't be the end of the world. At the end of the day there are other fabrication plants to manufacture microprocessors. And it's not as if China invading Taiwan would suddenly make all of the existing supply stop working.
