If the socket is rated for 20A, it will have 12 AWG wires. If not, then Ford is asking for a lawsuit when someone burns up their car. A good way to tell for sure is by looking up the amperage rating for the fuse in the aux socket circuit. 20A or higher and you're good to go.
FWIW, my 6666 pro hits 12A on peaks on SSB at the full 100W output and 10A full output on FM.
For a permanent installation, running wires direct to the battery is always the best way for lots of reasons regardless of what the socket says it'll handle. For a temporary installation though, you'll be fine.