And since that gas comes from one place, it is relatively easy to capture it and do things with it. Methane in particular can be burned, either to destroy it or even as a power source. https://en.wikipedia.org/wiki/Landfill_gas_utilization

At 1000$/tonne of CO2 (Air capture!) burying a soda bottle (2L - 42g) would cost on the order of 5 cents, or conveniently what many states charge as a bottle deposit, so no. You would have to be burying 5-10 kilos of plastic to approach even $10 worth of carbon dioxide emission mitigation.