I personally believe that forests provide a net positive in terms of CO2 scrubbing regardless of decay/decomposition. The only evidence I'd offer is a time lapsed NASA video[0] showing CO2 emissions heatmap over time. The areas like the Amazon clear up the CO2 on a daily and seasonal basis. The areas where forests are impossible like the Arctic, it does not. The sun drives the cyclical "heartbeat" effect you see from day to day on the video, where plants using photosynthesis in the day (and macroscopically, the summer) effects the intensity of scrubbing moreso.

Also, maybe it is my mind's desire to simplify of all of it, but it was eye opening for me, and seemed obvious upon seeing that video, that forests were the key player in air management globally, and industrialized nations were the main drivers behind CO2 production in the air globally.

[0]: https://m.youtube.com/watch?v=x1SgmFa0r04