Baking also tends to anneal the aluminum, which removes any heat-treating and makes the metal softer. Baking can also warp parts, either from leftover machining stresses in the part, or from uneven heating/cooling during the baking.
Personally, I wouldn't recommend doing it, but as long as you accept the not-trivial possibility of ruining or at least damaging the marker, who am I to say no.
Oh, and baking don't affect lasering. The laser basically burns off the thin layer of anodizing, or at least just the dye layer, leaving the bare or nearly bare aluminum underneath.
Baking simply heats the part until the dye in the anodizing breaks down, or even starts to scorch, which changes the color. In the places there's no dye- as in the lasered areas- there's nothing to change color during baking.