I don't see any reason why this wouldn't work for a hammock, but you have to be careful with technique so as not to light anything on fire or melt some nylon (yikes). If you're too high above the heat source it won't do much for heating you and you'd lose a lot of the heat to convection from wind under you and your tarp. It requires a pretty decent amount of effort to burn coals, dig out an appropriate area, cover it, etc. All in all I think I'd rather expend the energy to carry some extra down quilt weight
If I were going to try something that marries bushcraft techniques with hammocks I'd probably try the "supershelter" system FourDog has detailed in some other posts. If you're not familiar with it it's the Mors Kochanski supershelter adapted to a hammock; clear plastic tarp in front, reflective blanket/tarp in the back. Fire burning out front lets heat in through the front and bounces it off the reflector, creating a greenhouse effect. In addition to the efficient heating this type of shelter would block more wind so you have a double benefit. May not get to it this year but definitely on my list of things to try sometime!