Yes it could work. Actaully several ways. May be some old posts about it here also.
Another thing I have built smaller scale for testing but never built the full sized unit yet.
For alot of things, like leaves, you can let them dry naturally and just burn them in the wood burner. Most leaves burn clean as wood, fast and hot, when dried. People burn them fresh and wet in the fall when they rake them up and it's a nasty smokey fire that way. For fast heat to just take a chill off the house when a big long lasting fire is not needed I use leaves sometimes. Also old paper bags, old boxes, and junk mail. I don't do much for composting yet, though I do have acres of leaves I could use.
Well back to the composting,
"The extraction of heat might even regulate the rate of decomposition too."
OR it could stop or slow decomposition to an unuseable rate if your not carefull.
At one time I knew what the temps get up to inside those piles at times but forget now, maybe 190F or somewhere around that, perhaps it was alot more. Sawdust piles catch fire in Texas paper mills sometimes because of internal decomposition heat and hot summer sun. Been there, seen it.
Human waste and animal waste, dodo, crap, or whatever you prefer to call the stuff gets hot enough to kill the pathogens also in a proper pile, container etc..
Now, the same organic wastes also produce methane gas while decomposition takes place!
So rather you use leaves and grass clippings for a cleaner pile, or include dodo also it will do the same thing, safer for health without the dodo if you make mistakes or use mulch for food type plants.
Decomposition in the pile needs 3 things to complete properly. Heat which it makes itself, moisture which it normally contains, and air/oxygen which it uses up and needs replaced. The replacement of air/oxygen is why you hear people say a compost pile needs turned every so often, basically stirring in more air. Also to move the outer surface to the inner part of the pile, but mostly for air.
Now if you just toss a pile in the yard you will lose alot of heat to the air when you most want it depending on your inviroment, winter! It may even freeze solid in colder climates.
I used some 55gal barrels with removable lids, sealed well, tubing mounted to top for gas. Methane can be gained and used in a burner or to run a generator etc.. if done right and large enough system. I did different things with mine diffent times. I got some nice gas over time but not very fast, but that was a very small system.
If a nice big insulated box is built, maybe even add some solar heating, you could get lots of nice hot water or such from internal tubing in the pile. Make an easy way to turn the pile without tangling up the tubing. If the unit is sealed well you could even figure a way to extract the methane gas for some type of burner. At times you will have to add more air and stir the pile to keep the system working, how often would depend on many things, maybe once a month or once in several months.
Some foriegn countries in rural areas use the methane produced from septic type systems , you get the same gas from compost.
If your using clean stuff like leaves, grass, etc.. and don't care how long the pile takes you could set up a system as a preheater for your hot water tank year round. Just make sure the pipes won't freeze in winter and bust.
Perhaps use an old water tank in the supplie line, tap into the lower section with the piles tubing coil, and back into the tank at the upper secton. Let the pile heat the water in the coil and convection circulate it to the tank. The longer the water sits in the tank the warmer/hotter it gets. Could be a good preheater for solar water heating or after the solar heating system. If using convection to flow the water through the pile then the water tank should always have the hottest water, no reason for it to cool the solar heated water.
I forgot about it, but I was going to try heating the pumphouse this winter with several barrels of compost, tubing, a radiator, and convection flow.
Place the barrels on the sun side of the pumphouse in a box, radiator in the pumphouse. Put a thermostat on the light I normally use for heat to turn it on about 28F and see if it ever comes on this year. Got busy with other stuff and forgot about building it 
