CAMP APAYDIN, Turkey—When Syrian Col. Malik al-Kurdi fled to Turkey early in the revolt against President Bashar al-Assad, he joined an exodus of officers expecting to be equipped by the U.S. and sent back to fight the Assad regime.

Three years later, he and more than 1,000 other Syrian military defectors sit in a barbed-wire-ringed camp just inside Turkey, spending their days trading gossip and playing cards.

Rather...