Does a fallen tree left to decay release essentially all of its stored carbon as CO2 to the atmosphere? Or is the carbon uptaken by termites and bacteria, preventing its release to the atmosphere?
I Can't quantify the answer, but intuitively, nearly all of a burning tree's carbon is converted to CO2 - assuming the fire is hot enough. You are correct in assuming that termites and bacteria convert some of the carbon to other organic species, as do fungi, yeasts, moulds, and slow weathering. In addition, some of the rotting tree's carbon is converted to soluble inorganic ions, humic, fulvic and tannic acids. So no, organic decay would not yield the same CO2 as burning.
This would make an interesting school or 1st-year uni science experiment. Burn some wood in a sealed environment, measure the CO2 evolved, then repeat the experiment with wood in a wet organic-rich isolated biome, and compare the results. I suspect it would make for an interesting paper with potential climate change policy implications.
The key word in your query is the word "essentially". Termites and bacteria die too. So whatever carbon was initially converted from the tree into termites or bacteria ends up mostly going to CO2 also.
Of course some carbon gets converted to carbonate and that can combine with calcium to form the mineral calcite. The tree can also get buried in mud and over eons get converted to coal or oil.
It's not so much the amount of CO2 released but the rate at which it would be released that contributes to the Greenhouse effect. Burning will release CO2 faster than any form of natural decomposition
Burning wood for home heating could actually be a carbon credit. Wood offsets combustion of oil, natural gas, propane, and the use of coal fired generation of electricity. Wood left to rot, as the previous post note, is carbon neutral.
The idea that decomposers that consume the wood's carbon just die and release it is foolish. These decomposers are at the base of a complex food web that moves that carbon through a huge network. I haven't seen a study to quantify the amount of carbon released to the atmosphere, but it is an important question. I have seen many studies trying to get at the question of how much carbon is incorporated into the soil, but each situation is so different that it is hard to get a clear answer.
If organic matter is buried - such as in landfill - it will decay anaerobically, resulting in CH4 (methane) rather than CO2 (Carbon dioxide). Methane is about 30 times more harmful as a global warming gas. Hence the reason why it is important not to landfill organic matter such as paper, card or waste food. However landfill of plastics (which is generally derived from a fossil fuel) is carbon sequestration, resulting in a net reduction of global warming gasses. So waste must be sorted before incineration - incinerating plastics produces/releases much CO2 and drives global warming