Tried this out with a cheap carabiner and mason's line. Wow. This is a neat setup. You could attach the hammock exceptionally close to the 'biner or ring and thus have all usable length of your rope of choice.
Also using a carabiner you would have a spot to clip in a UQ or hang a stuff sack from, etc... Just a thought. I want to try this now with a better carabiner and amsteel and actually hang from it.