No – she did it in 72. After reading the Jules Verne novel Around The World In 80 Days, American journalist Elizabeth Jane Cochrane, who wrote under the pseudonym Nellie Bly, pitched the idea of doing it for real to the New York World in 1889.
The newspaper’s editor dismissed her, saying a woman would be unable to make such a trip. Biting back, Nellie replied, “Very well. Start the man and I’ll start the same day for some other newspaper and beat him.” The editor backed down and agreed to fund the journey. Departing New Jersey on 14 November 1889, Bly reached Hong Kong on Christmas Day. Here she discovered that not only had Cosmopolitan dispatched their own reporter, Elizabeth Bisland, to race her, but that they were three days ahead of her. However, Bisland missed a vital connection in England. Bly beat her home by four days, completing her circumnavigation of the globe on 25 January 1890.
However, while we today associate Phileas Fogg, the hero of Verne’s novel, with travelling in a hot air balloon, this doesn’t actually happen in the book. Instead it was perpetuated by the 1956 movie. Equally, she travelled mostly by steamship and train.