It's a common question - and the answer is no!
The fragrance oil that is mixed in to the wax does evaporate, sometimes you'll see a clear vapour coming off your burner as the fragrance is released. But the wax doesn't burn away as it does with a candle. That's why when the fragrance fades, you should allow the wax to cool before wiping it out of your burner.
Make sure you clean your burner well, but don't scrape the wax out, as scratching the burner can cause tiny surface cracks which can be dangerous.