You can do the same with a nuclear power plant and calculate how much power it generate and how much green house gases that represent if it was produced by a natural gas-fired power plant. Fuel cost is a thing, but to my knowledge they are fairly minor in terms of greenhouse emissions when compared to burning fossil fuels.

Batteries/storage do not produce energy so they don't displace any energy in this kind of calculations. They can be viewed as a small efficiency increase of existing wind turbines, in which case they do have a form of greenhouse gas payback time, although the energy must not be counted twice for both the turbine and battery, and the increased wear and tear on the wind turbine may impact the result.

Wind generally has an production rate of around 50%, which mean that countries like Denmark that has already reached over 100% wind production still only have energy for half of their consumption. This mean the storage need is fairly massive, which they currently solve by importing energy from fossil fueled thermal power stations, nuclear and hydropower from nearby countries. Constructing more wind power at this point does not seem economical for power companies, and any storage solution like lithium, reverse hydro, and so on are also not economical (as in, there is basically zero investment into it outside of government subsidized initiatives). As such, wind has in that location seem to have reached its ability to displace any more fossil fuel.