I wouldn't expect the battery to go flat in 2 weeks - though the airport (or similar) is not a good place to test this theory.
The only way of checking is to put an amp meter on the car, close the bonnet, set the alarm and see what the current draw is. Say it is 100 mA - in 24 hours, it will have drawn 2 amp/hours, so your 70 amp hour battery will be 50% discharged in 15 days. Now a 70 amp hour battery in good condition will tolerate that just fine, and will start the car, but a knackered one (that performs faultlessly when driven daily) will not.
I got caught when I put a new radio and bluetooth gadget in the 156. I got the permanent live wrong, but didn't realise as I drove the car twice a day. When I left the car for 4 days, it was flat as a pancake. The amp meter test revealed that it was pulling 750mA, so about 20aH a day - so flat in 4 days. After fixing it, the car draws 60mA with the alarm set, so will take about a month to reach 50% discharge.