What do you mean by "Han Chinese language"? You are aware that "Han Chinese" is an ethnic group that speaks quite a large number of langauges, yes? If by "Han Chinese language" you mean Mandarin, then it's important to remember that virtually no one on Taiwan spoke that language before the KMT showed up postwar. Most Taiwanese spoke Taiwanese Hokkien (usually just called "Taiwanese" 臺灣話), with a smaller number speaking Hakka, and of course small numbes speaking aboriginal languages.
It's true that Japanese was making huge in-roads during this time period. It was the language of education, it was the language you needed to get a good job or to speak to the government. It was the language of a wider culture, for reading not only Japanese newspapers, movies, and novels, but also for a growing body of Taiwanese lit that spoke to the colonial experience. Lastly, it was also very useful as a lingua franca, allowing the various language groups of Taiwan to speak to each other.
I know it's possible for languages to disappear and be replaced with their colonizer's language. There are examples of that around the world. But I wonder if it's really possible in Taiwan, at least during the time period we are talking about. During the Japanese colonial period, the government pushed Japanese hard--during the Militarist period, people were even strongly encouraged to speak Japanese within their own homes, and the Taiwanese-language newspapers disappeared. When the KMT arrived, they pushed Mandarin very hard, and Taiwanese was again strongly discouraged. And yet, Taiwanese is still around, still the first language of the vast majority of the people. I'm honestly not sure what either of those governments could have done to push harder. So I think Taiwanese will survive even if Taiwan turns into a normal Japanese prefecture or two, at least up until the present day. Maybe eventually it will turn into Welsh (for example), but just the 60 years since the war is I think too little time.