I made a blueberry muffin fatty after seeing it somewhere and it was fantastic. I like your idea. Mine had syrup added and I think that would be a must for your French toast fatty. Go for it and let us know!
I also make a blueberry muffin and syrup fatty as a dessert breakfast fatty after the traditional eggs, cheese, onions, and peppers fatty is demolished.
I normally do the prep work the night before. So I end up with a rolled up fatty or two in the fridge overnight. That honestly helps it set up and take a nice log shape. But I smoke them in the morning, wrap in foil, put them in a cooler filled with towels just like I do with my other bbq. I then take them into work for breakfast and no reheating is usually required.