When the ecosystem is somehow tapping into an ancient stockpile of high energy C compounds to oxidate, sure, it will release more CO2 than it consumes. An example of such an ecosystem would be humans doing agriculture boosted with the Haber-Bosch process, which oxidates fossil fuel to capture plant nutrients from the air (even our crops are not entirely solar powered).

Chemistry is incredibly simple when you are only interested in the general inputs and outputs of a black box system.