No! It's a valid question though.
Normally, we cook food on hot surfaces; therefore, a gas fireplace should be no different.
There are people who roast marshmallows over scented candles or hot dogs over a plastic-based flame. The thing is, we shouldn't be cooking those marshmallows or those hot dogs.
You certainly should not be cooking over a gas-burning fireplace.
And here's why!
For one thing, nothing should cook in a gas fireplace because it is chemically toxic so you're consuming those toxins.
Also, any grease produced from your food will fall onto your logs.
This grease will cause them to crack and deteriorate very easily because they shouldn't be washed.
It's possible that you'll have venting problem because there will be a layer of grease all over your fireplace and on things close to it.
Can you burn wood on a gas fireplace?
You shouldn't put anything in or out of gas fireplaces, including actual wood because by doing so, you could actually cause an explosion.
This is because the heat from the burning wood is prolonged and could backtrack to the shut-off valve, where an explosion would ensue.
In order to actually burn the wood, you need to completely remove the gas line and gas log from your fireplace.
In conclusion, it is not a very idea to cook food over a gas fireplace because it is dangerous not only for the safety of your home and fireplace but on your own.
So, if cooking with your fireplace is a deciding factor between buying a wood or gas fireplace, you should probably go with wood!