No, Taiwan has not been recognized by the United Nations as an
independent nation. It did once during China's communist revolution
in the 1950s-1960s. However, in 1971, China or "People's Republic
of China" gained entry to the United Nations. Thus, "Republic of
China" or Taiwan was expelled as a member. Taiwan has been trying
to get membership into the United Nations, but since China is
insistent that Taiwan is part of China and China is a permanent
security council member, they've been vetoing Taiwan's bid for
readmission.