The honest truth is liberal democracies do not come to fruition in vacuum, Elections are necessary but not sufficient condition for a functioning democracy. Afghanistan has multiple elections, Ukraine has elections, Iraq has elections, what is the state of affairs in these countries. There are subtle and messier parts in Democracy and every society cannot support it given their historical context - most societies have to evolve to certain point of maturity for democracy to take root and more years of practice of it to have it to work as intended.
It just sounds like excuses - which democratic country resolved all (or any?) of their problems with gender inequality, violence, alcohol, corruption etc. before instituting democracy?
In any case, Gmail is just one of many email tools - if Chinese people are so culturally unprepared to deal with Gmail, how are they culturally prepared to deal with QQ Mail, or Weibo/Weixin for that matter? This is just further censorship of a tool either for economic/protectionist reasons, or because it protects the CCP's hold on power. I'd struggle to see this as part of any plan to gradually implement democracy or as part of any uniquely 'Chinese' democratic development.