Yes, one can charge a house battery with a 4 or 7 pin connection.
But, not really a good idea for a standard equipped vehicle.
If your truck came with a single alternator, without any additional options for a travel trailer or camper, then you will be asking a lot of your alternator if wanting to charge house batteries.
First, an alternator in single installations is designed to maintain the crank battery and power the vehicle's electrical bus or distribution panel. An alternator scales its output based on demand by the bus and condition of the crank battery. Further, an alternator produces constant voltage for charging, 13.5 - 14.5. Not 3 or 4 stage charging as with "smart" battery chargers. As such, internal temperature of the alternator can stay relatively high for an extended period of time while charging vehicle and house batteries and powering the bus/distribution panel. Heat is the enemy of the stator in the alternator. Operating at a high temp for an extended period of time will ultimately lead to early failure of the stators. While the alternator operates at a constant voltage, resistance in the electrical system determines the amperage output of the alternator and its operating temperature.
For this reason, many of the HD domestic trucks provide for a second, or dual, alternator setup. Such a setup reduces the load on both alternators allowing each to operate at lower internal temperatures.
In dedicated overland vehicles, upfitters will often install a second alternator wired to a dedicated distribution panel for the travel trailer/camper house batteries/electrical system.
For the purposes of the OP, with his small electrical demand in the camper, going through a 7 pin would be the easiest method.