Not sure what you mean by a hose refrigerator... but most fridges are dual powered - 120VAC and LP (and also 12VDC for the control circuit).
There is no ill effect by shutting the gas off to the fridge, other than it won't run. If the switch is in Auto for example, and if 120VAC is present, the fridge will run on electricity.
But if you disconnect 120VAC, when in Auto position, it will attempt to use gas.
But, if you don't turn the gas on, you will simply get an error (blinking LED, etc) on the fridge that gas is not present.
Otherwise, no ill effect.
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