This article author doesn’t understand climate change. Carbon dioxide isn’t the primary cause. There are much more potent greenhouse gases like methane.
Plants don’t suck carbon from the atmosphere and store it in the ground. They store it in their plant tissue until it rots and it’s released again. This is like slapping a bandaid on a dam break. It’s a temporary sink and is such a small amount it’s not worth the emissions of the tractor used to plant it.
The clover won’t suck up the Carbon from the rye. That’s not how this works.
Cover crops are a good thing though. But not because of climate change. They help prevent erosion which is arguably a bigger threat to our agriculture than climate change.