If the biomass inside hugelkultur garden beds didn't decay, then it would just be a means of water retention. It does decay though, which enriches the soil but also releases CO2.

Hugelkultur can reduce demand for fossil carbon based fertilizer, but IDK if composting trees is economically viable without some level of carbon tax, or even logistically viable for meeting demand at the scale of modern, mechanized agriculture. It would be cool if it were though - paired with machines that run on liquid fuels created using renewable energy, fertilizer made from compost could be part of a zero net carbon system for growing food.