This is a subjective question, and will depend upon who you talk to and the type of business you intend to involve yourself in. Simply living in Taiwan. Of course, it cannot hurt to learn the local language; and, it could in fact open doors that you could not have opened without knowledge of the language.
For more a detailed discussion and evaluation, please refer to the Chapter 4 “Overview of How Easy or Hard it is for Foreigners to Start a Business in Taiwan” of the Book under the “Do I need to learn Mandarin?” subsection.
For the opinions of successful foreigners in Taiwan who have succeeded with or without knowledge of Mandarin, please refer to the Entrepreneur section of our website.
For a comprehensive list of Chinese learning centers in Taiwan and online Chinese learning resources, as well as lots of other useful goodies (such as useful Chinese words, terms, and characters), please refer to the Mandarin Chinese section of our website.