@Alpha Centauri is right. Pardon my omission: In each of my affected machines, the batteries still functioned, and the laptops remained generally operational. I used my warped laptops as they declined in their old age, though I would have fixed/replaced them if I'd known, then, what we now know about the volatility of LiPo batteries, i.e., the elevated risk of fiery explosion.
Be judicious taking apart a Mac with a warped case, even if it's just the lower cover. It might not go back together, especially if it's the swole-battery issue. The panels might not be simply twisted or bent, they might be stretched, and will contract when disassembled. Macs are so precisely machined, that even the teensiest divergence can ruin it.
If you suspect the swole-battery issue, consider just using Apple for the repair, if they're still capable. It will be expensive, but they should make short work of it. I used to charge right into DIY repairs, but now I attempt repairs only on gear I don't mind destroying.
If you suspect the case is simply warped, or the hinges or screen simply out of rack, then consider just living with it. Trying to bend it back might do the fatal damage, unless you strip the case down to bare metal. THAT is a daunting, error-prone chore, akin to working on wristwatches - for which one can at least still get parts.