Good advice above. However, if you insist on using an external charger, it will probably work fine without disconnecting the internal circuits. 12 volt DC power supplies usually work fine together. 120 volt AC power supplies rarely work together.
Note that there is no guarantee that the external charger is designed for long term optimal deep draw battery maintenance. Many automotive chargers are intended for less than 24 hour use.
Most RV's have excellent on-board chargers. They are well regulated. Many of the newer ones will drop output voltage to fully charged batteries to 13.2 volts for long term storage. 13.2 is the best long term float charge for lead acid batteries.
My on-board charger is a low cost WFCO. It lowers float voltage to 13.2 volts after about 4 days of constant very low current. Some more expensive models are programmable. A manual for the charger/converter/inverter may explain how to set it up.
I wish you good luck and happy trails ahead!