Yes, the filler will burn. It does burn a little bit over time even if you keep it wet, hence the disposable nature of cartomizers ;-) Try tearing apart one you've been using for a while and you'll see what I mean, there's also a few pictures posted somewhere of this.
It's best to top them off before you get to the fully dry stage, you should notice a slight change in flavor as you get to the point where it should be topped up