Actually I do this, and I do it because my oven is old and tempermental.
Adding a heavy heat-sink (like a pizza stone, or a half dozen fire bricks) to your oven will increase your pre-heat time, but it makes your ovens temperature much more stable. It's a good thing to do if you're planning on cooking anything that is really temperature sensitive.
I assume you are talking about the risk that the alcohol vapor from the wine mixes with the air and ignites.
Let's do some maths. I'll do my calculations with some pretty round numbers, but in the end you'll see that it doesn't matter.
Assume an average gas oven with a volume of 150l. According to Wikipedia, the absolute minimum mix of ethanol to air for ignition is 3%, so that's 4.5l of pure ethanol vapor.
Water expands at a rate of 1700 when it turns into steam. Assuming ethanol is in the same ballpark and add some entropy for higher temperatures, we'll assume a factor of 2000. That means we'll need 4.5l / 2000 = 2.25ml of pure ethanol.
In a typical bottle of red wine there is 12% ethanol, so for a 750ml bottle, that is 90ml.
As you can see, we have about 40 times the ethanol we need to make a nice boom.
Now to answering your question:
I would deem it probably safe to cook red wine in the gas oven. The burners are usually not in direct contact with the air inside the oven, and both the burners and oven is ventilated, so the ethanol would probably escape even before it could meet the required saturation. And even if the vapor was allowed to build up inside the oven and not get in contact with the gas flames, the self ignition temperature for ethanol is 363°C, far hotter than it'll get in there.
The most convincing argument that it's safe is the millions of times chefs around the world have cooked with wine in a gas oven :)
Best Answer
The US Fire Administration clearly recommends not leaving cooking appliances unattended when no one is home:
At the time this related answer was written, the Fire Administration said (they have since updated the page):