That could do a good job of turn signals, warnings for tailgaters, etc. I think putting up a message like "I support my local police department" might lead me to getting stopped.
One trouble I see is that the view out the back would be partially obscured, Probably the light strips would spaced such that 50% or so of light could get through, but if the strips were lit up either by themselves or something else contrast would be impaired. It would probably be OK with a rear-view camera but I wouldn't want to argue about that with the cops.
So for now I'll stick with a single LED strip mounted on the side that can replace my car's image with a McLaren F1 if somebody looks at it at just the right time in the right way.