A modern "inverter" fridge has a three-phase AC motors with, well, an inverter in front of it. It would be easy for the manufacturer to makes such fridges accept DC without a major redesign.
There's a good chance that such a machine may accept DC just fine without even knowing it. Assuming the inverter/VFD has a simple full-bridge as its first stage, the DC would just flow through the same half of the bridge all the time.
A lot of PSUs can do this too; I just bought a Mean Well RSP-1500-48 which specifies its input voltage as AC 90-264V, or DC 127-370V. This means I can run it straight from the traction battery in my car (200V DC) if I care to...
Many likely already do exactly that. It's similar to computer power supplies, which can often (at least if they don't claim active PFC) just take DC at 320 V if set to 230 V AC, because the current handling on the bridge rectifier is specified for 115/120V, which results in a their current rating only being half-used at 230 V.
Which reminds me to check a modern server power supply for whether it could just be switched over to a battery bank at a suitable voltage on power loss. Most load should be easy to shed in a couple seconds by triggering suspend-to-RAM, and UPS are wastefully expensive if they only exist to tank full load for a moment and standby/idle for long enough to handle manual filling and starting of a generator.
