Yes. Two numbers decide it: the station needs ~900 W surge output to start the compressor, and about 2,033 Wh of rated capacity per 24 hours to keep it running.
The 24-hour math
Average cycling draw
60 W
Energy per 24 h
1,440 Wh
÷ 0.85 inverter efficiency
1,694 Wh
× 1.2 headroom → rated capacity needed
2,033 Wh
Output needed (running / surge)
150 W / 900 W
Verdict: a 2 kWh-class unit runs a fridge for a full day; a 1 kWh unit covers ~half a day; add solar to go indefinite.
Why does a '150 W' fridge only use ~1.4 kWh a day?
The compressor cycles on and off; averaged over a day a typical full-size fridge draws about 60 W. Energy math uses the average; the output check uses the full 150 W running draw.
What's the surge and why does it matter?
At start-up the compressor briefly pulls ~900 W. A power station whose surge rating is below that will fault instead of starting the fridge — this rules out pocket-size units, not capacity.
How can I stretch the runtime?
Keep the door shut (obvious but dominant), freeze water bottles ahead of storms, and set the fridge a notch warmer. A full fridge holds cold far longer than an empty one.