in addition to what has already beensaid..... some vehicles are set up differently, and so some wont allow power to pass unless the vehicle is running, where others may just need the keyswitch on... and this is providing the circuit is active, as some vehicles dont have the fuse in it....
and then.... some vehicles will disconnect this circuit when the keyswitch is shut off, and others will allow it to be active ALL the time, which WILL drain your vehicle battery if you over use the power in the trailer....
but as for charging, the wire in this circuit will allow very little power back into the batteries of the trailer, because by the time the voltage and current gets all the way back to the trailer batteries thru the SMALL wire, the current and voltage loss will be such that there will be little force left in it to trickle itself into the trailer batteries...
having a "custom" circuit from the vehicle to the trailer plug is a much better option if you want to put a few more amps into the trailer batteries when traveling..
depending on how the "hot" wire from the tow vehicle is set up to operate, if the circuit goes dead when the keyswitch is off, you probable wont get as many amps replaced in the batteries when traveling, than you use in the evening... UNLESS you plug into shorepower...
if the circuit remains active all the time, as you use power out of the trailer batteries in the evening, the vehicle batts will suppliment the trailer batteries... then once you go to bed and shut out the lights, the vehicle battery will continue to drain into the trailer battery until they are nearly equalized... this is good if you are traveling everyday, but not so good if you are set up and connected for a few days, as it can discharge the vehicle battery to the point your truck wont start....
its my opinion that an added circuit with a #8 wire is a better choice for the hot wire from the vehicle to the trailer plug, which comes from a solenoid so its only active when the keyswitch is on, or the engine is running...