Yes, they can get a GPS stamp while in airplane mode. The current ENY Jepps app will still pull GPS data even with the iPad in airplane mode.
Who cares where you are when you call in sick? Europe? The Caribbean? On the lake in a boat? Your body doesn't give a damn where you are when it gets sick - and generally you are more likely to become sick when traveling. Airplanes with other sick people, hotel that a sick person stayed on, ill chef that should've stayed home preparing your food...
Doesn't matter. Sick is sick. What you don't want to do is provide any proof whatsoever that you planned on being at the location you are while you are supposed to be at work. I.e., multiple drop requests for specific days, then you call in sick for those days.
Better yet?
Turn your company iPad OFF.
Leave it at home.
Problem solved.