There are plans in Europe to run powerplants on burning wood to make electricity. The current rules for carbon neutrality allows this to be considered neutral as an activity but I disagree with that as an approach.
Whenever wood is burnt we dramatically speed the process at which the stored carbon is released. If do not burn wood it takes much longer for the wood to decay and release the carbon. The average time for a the carbon in a 100 year old tree to be stored is 50 years or so, if you burn it is released right away.
A 2x4 that is used for construction of building is likely to remain in place in that building for 50 years. Once the building is no longer needed the 2x4 is most likely going to end up in a landfill, though burning demolition waste is becoming more common. If the 2x4 does end up in the landfill it can decades longer before it decomposes. Realistically a 2x4 will store carbon for 80 or so years. This means in a 100 year old tree that is harvested the carbon will be stored for an average of 130 years which is 2.6 times as long as if you burn the wood.
The burning of wood significantly speeds up the carbon cycle. One has to remember that the trees cut down have not grown to the end of their natural life and the decay process in the forests is not a fast one. Finding 100 year old remains of trees in the forest is not uncommon. All timber harvesting speeds up the carbon cycle, burning harvested trees shortens it even more so. It is only an old growth forest that is truly carbon neutral.
In either case there is carbon being emitted which adds to the load already in the atmosphere and oceans. While the very fact that wood is part of the carbon cycle and is not a fossil fuel means it is an improvement over even the best fossil fuels it is still not neutral with respect to carbon emissions.