No, you can’t. It is not advisable to follow your instinct when it comes to charcoal stain. In most other stains, the first thing that comes to mind is to wet the stain so that it doesn’t set.
Washing charcoal stains with water right after it stained your cloth will spread the stains further to areas of the cloth that wasn’t affected initially. The best way to treat a charcoal stain is to brush as much charcoal dust as possible off the surface with a toothbrush or vacuum before later washing with water.