Nope. Plain old wars and good old fashioned political corruption did that.
The "drought caused the Syrian civil war" theory is, frankly, crap. It was based off of one paper, which built a big statistical mountain off of a molehill. They exaggerated the number of people affected by the drought, and failed to show any sort of cause and effect. For that matter, the ACTUAL cause of the migration was a financial - subsidies for diesel and fertilizers were cut.
The civil war in Syria, by the way, started two years AFTER the drought ended. If it was caused by the drought, it seems like the events would have been closer together.