You need to know how much you are drawing from the battery in order to answer that. Your WFCO is likely a 45 or 55 amp unit, how large is your battery charger? And can it keep up with your usage? Many small automatic units will give 6 or 10 amps for short terms but are not really able to give that much for several days, and will eventually overheat if the load is maintained.
If your portable is at least a 15 amp, and preferably a 25 you should be well covered. But it's just a guess since we don't know the sizes or demand.
You should be fine charging while connected, its a question of if it is enough.