A forest will be carbon negative regardless of how the harvested wood is used. Forests increase soil depth through dropping leaves or needles, and by light-starving prior growth. The trees also leave behind roots, a substantial fraction of the total organism weight.

The vast majority of carbon in a tree is from the air, so the sum is a net win. Most wood is also put to long-lasting uses, or made into paper which is eventually buried.

But even burning trees for power, while short-sighted, is net carbon negative, due to the first set of reasons I've mentioned.