While grid-scale electricity storage (hereafter 'storage') could be crucial for deeply decarbonizing the electric power system, it would increase carbon dioxide (CO2) emissions in current systems across the United States. To better understand how storage transitions from increasing to decreasing system CO2 emissions, we quantify the effect of storage on operational CO2 emissions as a power system decarbonizes under a moderate and strong CO2 emission reduction target through 2045. Under each target, we compare the effect of storage on CO2 emissions when storage participates in only energy, only reserve, and energy and reserve markets. We conduct our study in the Electricity Reliability Council of Texas (ERCOT) system and use a capacity expansion model to forecast generator fleet changes and a unit commitment and economic dispatch model to quantify system CO2 emissions with and without storage. We find that storage would increase CO2 emissions in the current ERCOT system, but would decrease CO2 emissions in 2025 through 2045 under both decarbonization targets. Storage reduces CO2 emissions primarily by enabling gas-fired generation to displace coal-fired generation, but also by reducing wind and solar curtailment. We further find that the market in which storage participates drives large differences in the magnitude, but not the direction, of the effect of storage on CO2 emissions.