I'm not sure if anyone has answered your question or not Wood Stove,
but depending on the manufacturer, yes you can fill them right up.
However... You have to realize that if you fill the unit up to the max you will loose out on your efficiency. So you will end up not getting as hot of water that you want.
The best thing to do is keep the amount that you burn at the recommended manufacture amount.
Also if you burn anthracite coal, you will get a much cleaner and hotter burn.