I guess that depends how you define 'Greatness', whether the word has any moral implications to you. He possessed the personality qualities of a real dictator, so if you consider 'Great' to be a function of significance and power and not of morality or overall quality of person, you could call him 'Great'.
I agree the glowing red eyes thing was a little over the top but I don't see his conversion as inappropriate for his character.
Dukat's thought process is like this: "I am awesome and ought to be important and powerful. Therefore, whatever means available to me to gain that power is who I am." First it was his military position, then his position in the civilian government, then his alliance with the Dominion, then finally it was the Pah'Wraiths. If he could have become important and powerful by playing piano music, he would have said he was always destined to play the piano, and that music burned within his soul.