Honestly, I think that's probably smarter than what I do now. My personal laptop idles around 15-20W, tends to peak at about 80W. If I bought a dozen laptops, the total energy usage would be roughly the same as my server at idle, and I could use Docker Swarm or something to glue everything together, while also having a lot more power resiliency because of the batteries (like you mentioned).
I also think it's good to prevent ewaste. There's a lot of raw computing power that just ends up in landfills. It's almost certainly better for the environment to get as much use out of existing stuff as possible than it is to buy new stuff. I can't imagine it's good for the world for a bunch of old lithium batteries to lie dormant.
If I can find a good deal on a dozen old laptops, I might honestly put this plan into action.