It's _possible_, especially in Taipei, but you'll want to take some classes before you go. I have non-Taiwanese friends who never learned Chinese, but they all regret it.
I find language learning fun though so it's definitely a feature, not a bug, for me personally.
Depending on what your skills are, some industries are conducted entirely in English.
Learning Mandarin has major benefits.
When I moved to Taiwan, I spent a non-trivial part of my time in Mandarin classes. It absolutely helped with daily life and connecting with other people even though my industry is one of those "entirely in English" ones.
I find language learning fun though so it's definitely a feature, not a bug, for me personally.