In the Flames of Vengeance part of the game, the answer is no. You can't access your dragon skills at all.
There is one point in Flames of Vengeance where the story forces you into dragon form.
Be sure to have retrieved all your dragon armor from your Battle Tower Coffer first (and you might want to make some health potions as well). If you want to re-assign dragon skills to different hotkeys, you'll need to pause the game and right-click the skill slot.
