Oh gosh, not quite.
This is a kind of cold war policy with caveats.
If China escalates militarily, US will likely tit-for tat and yes, may be involved in actual, armed conflict as it escalates Ex: China sends Aircraft carrier, US does as well, small gunboat firefights ensue, US participates, maybe some naval firing back and forth, Chinese marines found on Taiwan, US marines land as well, China does electronic attacks, US response.
But ...
In an unlikely 'Blitzkrieg' scenario, whereby China launches a very swift and unanticipated attack on Taiwan - say: multi-beachead marine landing, paratroopers, 5th column destruction of comms equipment, drone and cruise missile attacks, total electronic-warfare shutdown - and the Chinese have militarily occupied most of the major and important installations in say, 48 hours ...
Do you think the US is going to ramp up 500K soldiers and 'invade Taiwan'? It would be logistically difficult, and militarily questionable: the Chinese are well armed, and can fight, and landing beachheads in that scenario, so far from home, against a large enemy may simply be futile. In fact, the Chinese may possibly be able to easily defend themselves against very vulnerable US Navy ships these days.
The US/world reaction may be to use the US Navy to blockade Taiwan and all of China, and to launch electronic and economic attack on China.
But I doubt if the US would respond in a full-on WW3 scenario.
As the commenter posted, a gradual, even softer-than-Crimea takeover is much more likely.
Supporting pro-China elements in Taiwan, spending a generation 'educating' (i.e. propaganda) Taiwanese that they are in fact part of 'mainland China', using coercive economic incentives ... I think that Taiwan may ultimately join China through a slightly shady but nevertheless 'legal' popular referendum.
The Chinese have the advantage of taking a very 'long view' of things and can have '50 year plans' for such things. Western democracy unfortunately doesn't allow for that so often.