I doubt that one can beat the game with a single Red, Black, or Green Dragon stack. The late game bosses (Gremlion, K'Tahu and Baal) will give you very hard time.
K'Tahu's spit is about 3.5k Physical damage and even with a very powerful stone skin + magic spring on, it'll hurt, and you need your spell casts to damage the boss, not heal the dragon... Not to mention that you need to worry about his summons as well.
Baal has 80% Fire Protection (he's a demon afterall), which will make the Red and Black dragons look pitiful and when he summons demons, they will simply laugh at them (since demons have 50% or higher fire resistance).
However, the game is beatable with a single Bone Dragon stack, and has been proven already by Zechnophobe. The bone dragons inflict poison damage and few bosses and units have a decent resistance to it.
So, if you're willing to be a little bit flexible (meaning your strategy is not RD-based only), add a secondary stack to help the RD's from time to time
