It may already be wired to power your 120V outside outlet from the converter/inverter.
You maybe be able to do what you are thinking about. You will have to put some thought to rate of discharge due while you are driving, rate of charge while you are driving. I suspect you will be discharging faster that you are charging. How I will approach the problem:
Look at my full battery capacity, in this example 100 Ah; 50 Ah usable at 50%; discharge while driving -10A
charge while driving +2 ; net discharge is -8A
50Ah / 8 A = 6.25 Hours to get to 50%
You might consider adding a solar panel to top which will help to reduce your net discharge.
In summary, the decision is really about how many cold beverages you need when you are getting to where you are going.
2014 Ford F250 Super Duty, 6.7L Diesel, Ultimate Lariet package
2016 Forest River, Heritage Glen 272RL