Update: The answer to the question in the headline seems to be no, for now.
Following Egypt's severing of its main ISP connections to the Internet, Syria has now reportedly done the same. Possibly anticipating the political wildfire that has leapt from Tunis to Algeria to Libya and now to Egypt, authorities may be trying a preemptive block.
Syria certainly is a candidate for revolt: One of the real tyrants in the Arab world, it possesses an outsized security apparatus, little in the way of citizen rights, a smart, young population and a fear of the Internet.
Other sources, including Reuters, claim the Internet in Syria has not been cut off at the ISP level. Instead, the country is said to have tightened its already restrictive Internet rules, banning programs like Nimbuzz and eBuddy that allow access to Facebook Chat via mobile phones. Many services are already banned but access is often gained via proxies.
I asked Ammar Abdulhamid, a fellow at the Saban Center for Middle East Policy at the Brookings Institution and Syrian dissident about what's happening. Ammar follows movements in Syria closely and is in contact with people inside the country.
"I am still talking to ppl on Facebook, so it doesn't seem to be true, but it could still happen."
Like all wholesale shut-offs, if this is happening, it is happening in bits and pieces as the government severs ISPs or sites from their routers.
We'll update this story as we get more information.