My guess is no. Not now.
Even as the economic situation grows more strained in Cuba, government supporters have many mechanisms for control, from the media and the CDRs to the police and the military. Some Cuban officials have acknowledged waning support for the revolution among the so-called "Lost Generation" - the 2.5 million Cubans born since 1980, according to this report by former CIA analyst Brian Latell. But many Cubans have a stake in the socialist system and support it for economic, political, employment or ideological reasons.
Of course, it's impossible to predict just what will happen in Cuba in the aftermath of Hurricane Ike. Natural disasters have hammered governments before - look at how Hurricane Katina hurt the popularity of President Bush.
In another case, some analysts said earlier this year that Cyclone Nargis may bring down the government in Burma, according to this Newsweek report.
Newsweek also recalled the devastating impact that the 1985 earthquake had on Mexico's Partido Institucional Revolucionario. From the magazine:
After a massive earthquake hit, the authorities and the country's aloof president, Miguel de la Madrid, went AWOL for days, leaving citizens to organize rescue efforts themselves. When the president finally did appear, he initially announced that Mexico "didn't need outside help."
With more than 10,000 estimated dead, survivors had quickly taken to the streets to denounce the government's weak response. These protests energized a new crop of community activists and opposition leaders, lighting a spark that eventually brought down Mexico's long-dominant Institutional Revolutionary Party (PRI) years later.I don't think you're seeing a similar situation in Cuba. Raul Castro doesn't appear to be AWOL. He and other Cuban authorities have shown their skill in preventing hurricane deaths in the past. They are engaged and working to protect the populace. And even Fidel Castro, who hasn't appeared in public for more than two years, has gotten in his two cents, writing essays on the hurricanes for state-run Granma newspaper, shown here in Spanish.
Note: the image above was taken from the National Hurricane Center web site.