Charcoal can be used in a smoker grill as long as the smoker grill is not an electric smoker grill.
If the smoker is made for wood or charcoal then yes you can use charcoal instead of the wood in the smoker grill.
I have used charcoal in my smoker grill and it worked just fine.
However I much prefer to use apple wood to smoke my meats with in the smoker grill.
The apple wood makes the meats that are smoked in the smoker grill taste much better than smoking the meat with charcoal.
Smoking the meat with wood such as apple wood is also healthier for you than smoking the meat with charcoal.
But if you prefer to use charcoal in the smoker grill you can do so without any issues although the charcoal may take longer to smoke the meat than with wood.