Strictly speaking, the term 'carbon sink' refers to things that
remove carbon from the atmospheric carbon cycle. As the carbon in a plastic bag comes from fossil fuels, then at the very best, if we returned it
all returned harmlessly to the ground, plastic bags would be 'carbon neutral', rather than carbon sinks. But unfortunately making and transporting plastic bags chucks quite a lot of carbon into the atmosphere. Even disposing of plastic in landfill helps create anaerobic conditions for the decay of organic matter, which produces methane - a worse greenhouse gas than CO2.
Different plastics degrade at different rates, with some effectively not degrading at all. The carbon in biodegradeable plastic does end up as CO2, which is obviously a drawback (though of course so does the carbon in other plastic, when it's incinerated). The reason for preferring biodegradeable plastic is to help reduce plastic litter, which gets in the food chain and has a serious impact on wildlife:
Ocean plastic