A small amount probably won't do damage.
Briquettes can be smashed with a shovel, and carbon is good for the soil. But I pick them out and reuse them as fuel.
Keep in mind, though, that ashes have a very high pH and can goof up the composting and garden growing process. It's a good idea to add them only sparingly. A quart in a cubic yard of compost ingredients, for example.
Also, there are binders in briquettes, such as borax, which can, over time, build up in your soil if you use a lot. Small amounts such as what you put in shouldn't be a problem though. It's all a matter of degree.