It is true, but it also goes a little deeper than that. In the 1980s, Amy Yip, a Hong-Kong sexy actress, was extremely popular in Taiwan along with her nickname "波霸" (boba, or "the biggest balls" in Cantonese). Around the same time, people started to put tapioca pearls in drinks, and called the bigger tapioca pearls "boba."

In recent years, people do consider it's improper to use such a term and has been slowly moving to more SFW words as "大/小珍珠" (big/small pearls) in Taiwan, but "boba" has stuck too deep in the English speaking world.

Source: me, a Taiwanese in 30s that basically grows up with boba drinks