Tansmission fluid will and gear oil will burn to I also read on a $bt forum of people using hydraulic oil. I have read about synthetic not burning well they engine will still run on it but to much of it dose not burn and leves diposits in the exhaust.
as for the ash/carbon in the oil........ most ash that is in the oil will burn due to the intense heat and presure at wich it is burned. as an example look at a fire pit verses at wood burning stove when the fire pit burns out you are left with large chunks of charcoal when the same wood is burned in a closed enviorment(wood stove) it burns to a very fine ash.
I have ran both WEO and transmision fluid in my truck first in lower amounts 5 gal in a full tank. did not notice a differance. then when It got down to below 1/4 tank I put in 5 more gal of oil atf mix and it seem snappier. and smelled like buring oil

Milage was the same just a little more black smoke with the pedel to the floor.
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