Short Answer : If your hammock is a "camping" hammock , or is made of parachute material, almost certainly YES. (Eno, Kammok, Grand Trunk, Bear Butt, etc...) ( even the Crua Koala!)
Long Answer : The Swiftlet is designed to hold most modern hammocks. The Swiftlet can fit hammocks between 106" and 140" in both short and long mode. This falls short with traditional rope "European" style hammocks with the large spreader bars at each end. A good way to test if your hammock will work with the Swiftlet is as follows : at 96" (48" each way from the center of your hammock), can your hammock compress to fit in your hand? If so, it fits with the Swiftlet! If not, it does not fit.