Physis,
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I don't think electric cook elements have much inductance so I'd suspect you wouldn't have nuisance tripping.
Over here in NZ, there has been a problem with protecting Electric Ranges with an RCD (GFCI).
The problem is moisture getting into the internal wiring after the appliance has been used and starts to cool down.
This moisture can cause leakage currents that will trip an RCD.
Bear in mind that this problem was found with indoor cooking appliances, so an outdoor one would tend to be worse.