Sometimes. From Helen Gordon at Wired:
Long thought an impossible dream, the emerging field of palaeocolour is revolutionising our view of the prehistoric world, turning it from black-and-white into glorious technicolour. So far only a handful of dinosaurs, insects and reptiles have been studied but, as Johan Lindgren, a scientist from the University of Lund, says, “We’re only just scratching on the surface.”
Finding evidence of colour in the fossil record will do much more than simply tell us what hue to paint a T-Rex. Bones can fossilise. but behaviour does not. “When we look at the animals and plants we see in the world around us we see striking colours and colour patterns,” says Maria McNamara from the University of Cork. “Animals use colour for camouflage, for avoiding predators, for mating signals and also for signalling within their social group. So evidence of colour in animals has the potential to tell us about this very enigmatic aspect of the biology of ancient organisms.” More.
Faint traces are better than nothing. Beginning to fill in the picture and may shed light on behavior in dinosaurs:
For instance, it had long been presumed that the small, four-winged Microraptor was nocturnal, based on the large size of its eye sockets. Then Vinther, Quanguo Li from the Beijing Museum of Natural History, and colleagues, discovered that the dinosaur possessed iridescent plumage (an example of structural colour) – something that would make no sense if this dinosaur were active only at night.
Or, in the early stages, new finds at least create something concrete to argue about.
See also: Researcher: “[i]t’s amazing how clear cut the change from ‘no dinosaurs’ to ‘all dinosaurs’ was.”
and
Dinosaurs are tearing paleontology apart?