No. There's a breed of dog called a Great Dane (which is actually German), so it would be appropriate to say 'a black Great Dane.' Obviously if you had a fantasy novel with dragons where they were classified by color or there were Greater and Lesser Dragon breeds, you could set your own rules of usage, but in the abstract dragons have to be treated like any other noun.
It seems to me that you agree with Swizec. 'Great Dragon' sounds just like 'Great Dane' when you put other adjectives. Certainly to my mind it sounds like it's a particular species of dragon. Given that the only place green-coloured dragons live is in fantasy (the komodo isn't green), there's pretty free reign to interpret it.
And in the context of animals, it's particularly unusual to use the adjective 'great' by itself, without it being part of the breed name. 'Great big' maybe, but rarely just 'great'. If you saw a large bulldog, it would sound strange to call it a 'great bulldog' instead of a 'great big bulldog' or other adjective.
This being said, because of their most prominent colour, we can talk about "gray great white sharks", and get the colour in on both sides :)
You're quite correct - I realised about five minutes after posting that what I wrote is really about when you want to use 'great' to mean 'larger in size'.
If someone says "I have a great bulldog", it generally means a bulldog that's excellent in some way. If someone says "I have a great brown bulldog", it's more likely that they're now using 'great' to talk about size.
