Are you mathematically adept? It will help if you are to do the analysis of your question.
In fact I will not answer your question because it is simply yes, yes and yes. One needs to be careful in the domestic setting about schemes to store electricity in useful amounts in batteries because it has high capital costs. Thus one has to be convinced that the return on this capital investment is better than something else you could do with the same expenditure. Folk often do not factor in replacing the batteries, housing the installation, equipment defects and repair, under utilisation ie you do not take advantage often enough of the saving you have attempted to make by your investment worthwhile.
On the green agenda I have not seen any scheme to sustainably shift towards batteries by recycling or reusing them. You can search on line and find firms which will offer you batteries previously loved in ev cars but their performance, quality and reliability is vague.
Unless you really can demonstrate it is a good investment then I would caution against storing mains power during off peak periods for use during expensive periods. The analysis I did last month for my home did not convince me - but I am fallible.
If you have solar power in excess there is some merit in storing some of it if you can reliably use it in quantity later and thereby avoid that consumption from the mains and the economic saving justifies the capital expenditure.
A great combo for solar pv is with air conditioning - which is the West Coast of USA experience.
I like others moan about the daily standing charge which has gone up. I think it is about 20p for us each day. But put in perspective, for that 20p I have access to a supply of up to 12kW every second, every hour, every day........I'd find that impossible to achieve for 20p a day at a reliability of something like 99.9%. My mum and dad in a Northern town have never in 20 years had a power cut. We get about one 5 minute power cut a year in winter. You would find it hard to invest yourself for your requirement to achieve those levels of availability and reliability and capacity of electricity. You could invest in being largely off-grid but be prepared to change your behaviours and life-style in your consumption - these have costs/implications too.
Food for thought. I do not have time I am afraid for a discussion.