That's at the extreme of unlikely.

The carbon that we're digging up was in the atmosphere before, it has just been sequestered, we're returning to a state that the Planet has seen before.

Across the entire Earth's history we're still at a fairly cold point and a long way from "Greenhouse Earth" and the temperatures at the Eocene Optimum.

And according to the IPCC: "a 'runaway greenhouse effect'—analogous to [that of] Venus—appears to have virtually no chance of being induced by anthropogenic activities"