Of course it does, in some areas. Most Syrian's who are in war torn areas are using sattelite internet anyway which connects to neighbouring counties afaik. Even normal internet connections in Syria pre-war/uprising was terribly rubbish, used to cut out at multiple times of the day. The thing is the internet companies are owned by the government so yeah.
I'm sure they have datacenters and computer rooms there, though I wouldn't want to host there. Too much unrest and turmoil right now. I'd hate for my remote hands staff to get caught in the middle of some pissing match and get murdered on their way to replace a failed drive, and I'd hate to have anything important there until (or if) this all blows over.