Yes, because more methane gas is released to the environment directly.

Did you read and agree to this book informations about your item?

2001 The potential of U.S. grazing lands to sequester carbon and mitigate the greenhouse effect R F Follett; J M Kimble.pdf

The most controversal and spectacular answer to overgazing dry grassland I found by https://en.wikipedia.org/wiki/Allan_Savory.

See this articles available by my links down here:

Did you already hear about this ecologist and his ideas that are widespread by the web and what ist right and what false? I think he isnt fully false with his experience.

J HUMER

in Austria, a landscape with many mountains and high developed farm pastures 

https://www.theguardian.com/environment/georgemonbiot/2014/aug/04/eat-more-meat-and-save-the-world-the-latest-implausible-farming-miracle

https://www.ted.com/talks/allan_savory_how_to_green_the_world_s_deserts_and_reverse_climate_change?language=de

http://www.regenerateland.com/2015/12/14/why-the-slate-article-about-allan-savory-is-dead-wrong/

http://www.deutschlandradiokultur.de/mahlzeit-wo-rinder-weiden-waechst-kein-gras-mehr-falsch.993.de.html?dram:article_id=366037#

Yes, the heavy grazing had a potential to increase C storage in rangeland ecosystems.

Dear Mouldi,

Can you explain the process (based on scientific evidence)?

Best, Mounir

For more explanation, see chapter 4: Inorganic Carbon Sequestration in Grazing Lands in: The Potential of U.S. Grazing Lands to Sequester Carbon and Mitigate the Greenhouse Effect. Again, you can see: Response of Organic and Inorganic Carbon and Nitrogen to Long-Term Grazing of the Shortgrass Steppe.

Best, Mouldi 

Long-term grazing at the heavy stocking rate would result in increases in soil C and N because those species that increased with heavy grazing have higher root-to shoot ratios than other plant species commonly found on the short grass steppe.