Burner assemblers and labs work well.
Burner radars, lamps and pumps don't work. Inserters try to fuel them but fail.
Burner beacons don't work either, and inserters don't even bother trying to put fuel in them.
The screenshot below shows the test, with inserters trying to insert coal from chests. Labs and assemblers work, radars, beacons, lamps and pumps don't:

(as a side note, it's also impossible to make burner laser turrets, roboports, and combinators. They automatically switch to electricity.)