No Ford will not do a thing, because the car makers (unless it's a special case....see Porsche and the Enduracers rFactor mod, or Ferrari and BATRacer) don't exactly make a habit of slapping down mod teams. Ford frankly do not give a crap whether you use a CVPI, a PD however does.
Okay, so going by your logic nobody should post pictures of cars on FB or Photobucket or deviantART or wherever since...ya know, it's copyrighted. However the car makers do not take down those images. There's something called 'fair use'
Obviously, if you go posting images of your brand new Porsche cop car all over the internet and say you're making it to be released, you are going to get a letter from Porsche AG and asked to stop and delete all the work (as Enduracers did and complied). Whereas, post pics or photos of a CVPI, not a whole lot will happen.
Why? Because, CVPIs are common, they've been done in a LOT of games/movies/TV shows/books, whereas the luxury car makers...which Ford is not one of, are more aggressive about protecting their brands. For instance: Ferrari barred Jalopnik from covering their cars after Jalopnik published an article questioning Ferrari's ethics, i.e. bringing track prepared race cars and disguising them as road cars. End result? Ferrari blacklisted Jalopnik from writing about their cars.
Ford have bigger fish to fry than a Youtuber uploading a video of a game mod using their cars, when they have bigger problems on their hands, whereas Ferrari and Porsche (and to a lesser extent BMW and the whole V.A.G, Volkswagen Group...which is stuff like Bugatti, Porsche, Audi and VW) are some of the most protective of their brands.
So if you do a Ford badge you'll get sued? That's like Nike going after someody for modding Niko's shoe textures. Not going to happen a whole lot.
As for the LCPD comment, you put the LCPD site, not LCPDFR, so I was making the point that the actual LCPD is a bunch of pixels and code, so would they really care what another PD thinks?