Is this historically accurate?
Yes, this is historically accurate. Writing on bamboo slips was not entirely abandoned until the 4th century CE---over a century after the Romance of the Three Kingdoms takes place. As the Wikipedia article on the history of paper that you linked to states, the primary use of ancient Chinese paper before this was for wrapping things, not writing. One of the largest collections of bamboo and wooden slips to be found (140,000 pieces from Zoumalou) dates to the Three Kingdoms period.