Interesting drawing shows where the carbon is and how much flows into other compartments:

Carbon Cycle

It's complicated and burning fossil fuels is a small but steady flow. Even though much larger amounts of carbon move between plants and the atmosphere, and oceans and the atmosphere, those flows are about equal. The important part of it is we are adding 9 billion tons of carbon to the atmosphere, of which 3 billion moves into the soil and 2 billion moves into the ocean. If we cut off all of our carbon emissions, presumably those flows into the soil and oceans would continue, but slowly diminish over many years as less carbon was in the atmosphere.