I'm sure someone has made a "silk purse" out of a pig's ear just to prove that it can be done. But you wouldn't want to carry it around. Future generations won't have a clue what "composite" or "NTSC" or "PAL" used to mean. An RCA ("Cinch") connector will be just as "retro" as a tie-dyed shirt or a glass milk bottle.
you can get chips with enough horsepower to do simple composite video AND computing and other I/O
If you are interested in mass-producing a product, there are probably more suitable chips than Arduino/Atmel. For roughly the same price as the Atmel chips that Arduino is made for, you can get chips with enough horsepower to do simple composite video AND computing and other I/O. The Arduino folk likely chose the Atmel chips they are using more for the ease of programming than for the performance bang for the buck.
One that I've seen recently is: http://www.xmos.com/