If plugged into 120V AC power source then your trailer converter supplies the 12V DC system AND charges/maintains trailer battery
When plugged into your F150 the 12V DC power line via the 7 pin connector will help maintain and charge your trailer battery provided your F150 trailer power Fuse/Relay has been installed AND trailer battery is NOT run down...low voltage.'
Truck charge line is limited due to size of wire and length of wire.
Look in your OWNERS MANUAL for trailer power fuse/relay location and check that it has been placed in the fuse panel
One 12V battery is good for about 1 1/2 maybe 2 days of DC Power then will be needing recharging ---unless you run furnace then battery is good for 1 night (maybe)