Hi,
Yes, aquatic plants do in fact need carbon among many other nutrients and trace elements such as nitrate, potassium, iron, etc. Carbon is produced by respiration of all living organisms in the tank such as fish, snails, bacteria, and the plants themselves.
Additonal c02 can be introduced artificially via Excel (a liquid product) or by c02 gas.
I would advise against using charcoal as you described as a source of carbon for your tank.
Hope this helps.