If you convert Power to Gas in the form of LPG or methane you then burn for energy when renewables aren't working, you're kinda defeating one of the main purposes of renewables - low carbon output.
No, you are carbon neutral. The most obvious (though maybe not best) way to do this is turn separate water into H and O, then store the H in a tank. When you need more power you burn the H getting water back. This process is not very efficient, but when power is cheap who cares.
You can also turn CO2 into synthetic oil (Methane, gasoline, Jet fuel, motor oil - your choice of what you want) via known processes. Again the process isn't very efficient, but when the inputs are free who cares. The sum of is carbon neutral.
In order to convert elecricity to methane you first have to REMOVE CO2 from the enviroment. If you subsequently burn that gas, you arrive back at the CO2 level you had before the P2G process.
That of course only works out to net zero when you use co2 that was recently captured, like from waste-biogas or trees.
The big problem with fossil fuels is not directly that they release CO2, it is that they release CO2 that was captured over millenia in the comparatively short timespan of decades.
You can avoid that problem entirely with P2G systems.
You can also turn CO2 into synthetic oil (Methane, gasoline, Jet fuel, motor oil - your choice of what you want) via known processes. Again the process isn't very efficient, but when the inputs are free who cares. The sum of is carbon neutral.