The way these trucks are wired is the alternator is hooked directly to the batteries (in the big red junction box near the power steering pump). The ECU controls the alternator, so as long as the engine is running, the ECU will command charging, even if the ignition switch is off.
You can always verify this with a multimeter. Hook the multimeter up to your battery, hold the hood sensor down so it can start, and remote start the truck. Be careful nothing gets sucked into the belt, etc. You should see the voltage come up to 13+ volts within a minute of remote starting the truck.