I honestly would be very surprised if they didn't make more CO2 logging and turning that tree into a building product than they sequester. Postal spam is likely even more damaging.
Trees are roughly 50% carbon by weight. Each pound of carbon represents 3.67 pounds of cleaned carbon dioxide.
Each pound of lumber represents 1.8 pounds of carbon dioxide our of the air. It looks like both logging trucks and flatbed timber trucks can carry around 24 tons of lumber, which would be 43 tones of carbon dioxide.
Sawmills are efficient, and would make a negligible contribution to total carbon. Transportation would be the biggest carbon cost. At least on the East Cost US there's a lot of timber growing so distances aren't too far. Let's say 200 miles total from logging to sawmill to use. 400 miles round trip. Using average US freight truck emissions that's about 0.07 tons of carbon dioxide released.
So let's round that up a bit and say 43 tons sequestered for for 0.1 tons expended. Seems like a win.
You haven't sequestered anything by getting it to the sawmill, that's only one portion of the journey. Also Using the Environmental Protection Agency’s Greenhouse Gas Equivalency Calculator, one ton of carbon is equivalent to 413 gallons of gasoline, so I think your math is off.
You can't get ahead if you're pulling carbon out of the ground. That's the fundamental problem. Go ahead and burn all of the carbon you want, as long as it's not coming from long-term storage (e.g. fossil fuels), and is rather already part of the carbon cycle (e.g. trees).
