Charcoal found to be supported
This PR adds the text that charcoal is supported, as in CC: Tweaked version 1.113.1 an advanced mining turtle took charcoal just fine in place of coal. Untested right now if other fuel sources work as well.
A lot of different items can be used as fuel by turtles, the limitation isn't in the mod, it's in the script. The script has a system where it automatically refuels the turtle using the coal it mined, meaning that you don't have to refuel it manually. However the system isn't very flexible, it only supports coal, and with the current system the turtle can even intentionally drop other types of fuel to free up space for coal
So no, charcoal isn't supported. With that said, I've just realized that I completely forgot about #13 which adds proper support for other fuel items. You might wanna try using the code from that PR if you want to burn charcoal