The two have plenty in common: both are effectively independent, democratic states in close proximity to much larger, authoritarian states with a plausible (if hardly uncontested) historical claim to control them. Are the similarities between them greater than the differences?
The latter are: Taiwan, in spite of its unpromising beginnings, is a more impeccably liberal democratic state; Taiwan is the sea gateway to Japan and South Korea, whereas Ukraine has far less strategic significance to the West; and Ukraine is impossible for the West to defend without an all-out war with Russia, due to its lengthy land and sea boundary with Russia, whereas the assumption has always been that America’s air and sea supremacy was enough to protect Taiwan from a Chinese invasion.
In short, the answer is no, but the question is getting closer, due to the increase in Chinese military power. America is never going to go to war with Russia over Ukraine, any more than it went to war with the USSR over Czechoslovakia or Hungary during the Cold War. What will happen with Taiwan is not currently foreseeable.