Let me start by saying that this is one question that has not given me peace of mind. I have tried many different approaches to producing this extremely rare effect. Believe me. Getting this effect was not easy. I made over 60,000 attempts to use Stuffed Dragon, and not one of them produced the effect:
You... will.... burn!!
But after many attempts I finally managed to find the answer to this question. It turns out that I was probably using Stuffed Dragon in the wrong way. At first, I kept my Stuffed Dragons in my backpack and used them with a hotkey.
I used this method to make those 60,000 attempts. Without success. In another question on TibiaQA user Smucker presented a screenshot on which we can clearly see how Stuffed Dragon causes the sound "You... will.... burn!!". I will honestly admit that this surprised me a lot. Smucker also presented his method for causing this ectremely rare effect. It turns out that probably the Stuffed Dragon when it is used must be placed not in the backpack but on the ground.
So I put some Stuffed Dragons on the ground and started researching this method. During testing, I used a character that had 1HP to be able to answer just the question above.
I do not know the exact number of attempts I have made with this method. But certainly the number was more than a 1000. And it's finally done!
Yes! A fire effect appeared on my character, and the Stuffed Dragon made a matching sound. To my surprise, however, I did not die.
As you can see in the screenshot below, I was not wearing any Equipment that could protect me from the fire.The screenshot below also shows my character's HP and Server Log.
As you can see this is proof that I did not receive any damage and therefore we can already answer the question clearly:
Nothing will appear in Death Log because using Stuffed Dragon cannot kill you.