If you can leave the RV plugged in all Winter, the battery can stay connected. When fully charged the battery will not freeze.
The 7345 just provides a steady 13.6 volts. This runs all accessories and will keep the battery charged.
Other things will discharge the battery if it is not charging such as propane detector, radio memory and appliance control boards.
An inverter uses battery power to make 120vac. This only drains the battery. You apparently do not have an inverter. Some larger inverters also will charge the battery when you are plugged in. This you do not have either. 7345 is just a converter that uses 120vac to make 13.6vdc.
