There was a real TTA that sold for pennies on the dollar last year(?) It was painted black, but the jams and all were still original white. It looked like a nice paint job, but it wasnt completely painted.
If you were to paint it, it would have to be a full tear down and then paint every nook and cranny for it to be a success.
Would it hurt value? I dont think so. Painting a car now days is very expensive and if its a good job and done correctly, then it will increase the value.