MCShrum, if you are talking about lump charcoal, made from whole pieces of wood, then yes, you can (I think we are talking about the same material - not briquets). I have done so myself. This materials tends to come in big pieces that are easily reduced (outdoors) with a hammer. Far cheaper than the horticultural charcoal products.

A caveat, though. You do need to read the package carefully before you buy. There should be no "'lighter fluid", paraffin, or similar materials added to make it light faster. Stuff that is essentially made and promoted as a natural charcoal should be OK. Inspect the material once you get it home, if there is a fuel-type odor, don't use (except possibly for grilling steaks or chicken).

Depending on how much you want to fuss around with it, you can also make your own charcoal. Get a strong fire going in a charcoal grill, have small to medium cut-up pieces of hardwood ready, add these to the fire, once the wood catches, put a lid on and cut off the air supply. I have made a lot of charcoal for orchids this way.