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Can a 100Ah Battery Run Starlink?

Usually yes, but not for as long as people expect once a fridge and other camp loads are included.

Quick estimate

A 100Ah LiFePO4 battery stores roughly 1,280Wh, with about 1,150Wh usable in a conservative setup. If Starlink averages 55W for 8 hours, that is about 440Wh. Add a 12V fridge at roughly 400-600Wh/day and the battery may be mostly used in one day.

Better recommendation

For Starlink plus fridge weekends, 200Ah is usually the more comfortable minimum. Add 200-400W of solar or a DC-DC charger if you will stay parked for more than one day.