Depending on the conditions, if you're doing day-night energy storage, then you would like to fill up the H2 tank and then burn it when demand ramps up.
The only role I see for methane is when your H2 tank is already filled up but your solar panels are still producing. This is not just possible, but deterministically required whenever solar gets deployed enough for seasonal storage to be necessary.
Right now California is something like 35% solar + wind energy, and the "duck curve" is nearly maxing out. This was predicted in extreme specificity 20 years ago, as >30% and you get stuff like zeroed-out energy prices during the day. We have not solved the day-night (daily) energy storage problem, which only requires storing energy for a matter of hours.
When you go to something like 60% renewables, then even crazier stuff happens. Overproduction during sunny times goes bananas and (assuming daily storage is solved, which it isn't) seasonal issues start to arise. I don't think H2 will ever work for seasonal storage, although I think it's fine for multi-day storage scenarios. It's not theoretically impossible, I just compare to the equivalent that we have for natural gas and realize you would need MANY TIMES that level of investment to save the same amount of energy in H2. Plus, fossil fuel gas producers are mostly at a constant level, whereas solar production outright needs summer-to-winter storage.
What I don't buy is that these units will be disconnected from the grid and be economical by their gas products. No way, no how. What you want is to run the chemicals plant with low-voltage solar power locally, and trade-off with the grid as is economical.