Why not just a 20kWh battery for energy time shifting. Or are you looking to sell the hydrogen?
But indeed, no, this just doesn't work. Best available efficiency for round-trip electrolytic fuel production / electricity generation is 40% or so, meaning that those roof panels wouldn't be enough anyway. (Also there's the problem of having every home store a winter's worth of pressurized hydrogen or whatever on-premises. Yikes.) It's not worth it.
Home solar is attractive because unlike most infrastructure it scales down really well and is actually feasible to do at the level of an individual user. But, like most infrastructure, seasonal power management is a grid-wide problem and needs to be solved at the utility level. There are plenty of tricks available there that homeowners don't have access to.
Such a system would be unlikely to ever payback for itself. Not deluding myself on that one.
FWIW: net metering seems like "trash tier" precisely because that summer PV excess really is mostly wasted (this is true for big panel farms too). The utilities were taking a huge haircut on the old 1:1 billing that California just rolled back. It wasn't sustainable.
What to do in the winter? If the answer is "use the grid", then we just kick the can to someone else, who will probably use fossil fuels to provide the energy. The basic problem remains - solar/wind are intermittent and fluctuating.
However until zero kWh is generated from fossil fuels in summer, solar/wind and battery is a massive gain, even if gas is still used for 2 months a year.
Efficiency is irrelevant. The only thing that matter is cost and feasibility. The cost of energy from solar is ~$0.02/kwh and sometimes even $0.00/kwh (when the grid curtails production). Even with 30% efficiency each kwh retrieved from storage will cost a record-low of $0.06/kwh (3-10 times lower than the consumer price).
The biggest factor here is the capex and ease-of-use of the equipment. Not the energy input cost.