Hi Gower, the olive oil probably won't hold up too long but it does look good and it's easy to apply. You should also keep an eye out becaue it can turn rancid since it doesn't cure; this is the biggest drawback of using food oils for finishing. Usually they aren't recommended but I'd say now that it's on just see how it goes, you may not have any problems.
Most finish deterioration comes from the sun. If your barbecue is covered you don't have to worry. Otherwise a finish with UV inhibitors is a good idea (all finishes are non-toxic when cured and safe for indirect, non-intensive food contact) but then again if you really want to play it safe go with an edible finish. Two solutions are pure tung oil or pure boiled linseed oil. Here in North america if the container says "100% pure" there are no chemical dryers or additives. We also have "Tried and True" varnish which is made from pure linseed oil.
Just a few thoughts,
Frank