The fundamental question that the study ask is if the wind turbine would replace an existing natural gas-fired power plant, how much less green house gases would it produce compared to keeping the natural gas-fired power plant, and how does that compared to the production emissions of the wind turbine.
Battery backup isn't a needed as much as many thing in the real world. Those gas power plants we already have are not going anywhere, so we still use them when there isn't much wind. Though battery is something we should be building instead (and are).
Instead, civilian energy demands and energy independence are the motivating factors. Look at how Ontario leveraged its electricity supply in the early days of the trade war.
https://world-nuclear.org/information-library/country-profil...
When you also add the cost of battery backup.
Spain and Portugal have just experienced the first taste of that fact.
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.