If you connect a battery to a converter only, you are pretty much guaranteed failure of the battery, and possibly filling your TC with poisonous gas from the battery as it fries.
I am not a "Sky is falling" kind of guy, but I really think you should do more research.
At the very least, do not charge the flooded wet cell while it is in the TC, do install a disconnect switch so only your converter or battery can be connected to your 12V system at the same time.
I am moving this Thread to the Tech Forum, so you can have more input as to what you want to do.
Wayne
Moderator