Hmmm i'm not sure exactly how it works because im from lebanon, and when i was in lebanon initially with just my canadian passport i couldn't get into syria without a visa, which costs around 50 dollars i think. This year however i applied for a personal ID card in lebanon and got one, which allowed me to get into Syria with only that card as a Lebanese citizen, not a Canadian one, so i didn't require a visa!
I agree with arachir call the embassy and request more details so you can be prepared to either apply now and have it in time, or get it right before you want to go there!