Depends…
Coal burns hotter than wood so you might burn out the grate (if there is one) quicker (sometimes a lot quicker) than you would if you stuck to wood.
We've got three (relatively) cheap wood burners from Machinemart installed in various parts of the house and I regularly burn coal as well as wood on all of them. If you keep a reasonably thick layer of ash/slag between the coal and the iron body you'll probably avoid burning a hole through the bottom too quickly.
Generally the more sophisticated (i.e. expensive) the wood burner is, the less tolerant of coal it will be.
At the end of the day it's just fire in a box isn't it?