@wytelyon I don't know, but that reminds me of a RAM expansion card for the Apple II that had an optional external lead-acid battery that would keep a RAM disk powered even when you turned off the computer: Product brochure

Crucial used to say, "As a rule of thumb, you want to allocate around 3 watts of power for every 8GB of DDR3 or DDR4 memory." (now that page just gives a more generic 5W per module estimate). That's too much power for a CR2032 battery. From my experience with powering my e-paper badge with a pair of CR2032s, you can only get a few mW out of them. So I think you'd need something like a Li-ion battery to power RAM.