I don't know of any canonical answer for this, but the amount of calories in blood, even if you drained all of someone's blood, is relatively low, probably not even enough to sustain an undead creature, even assuming that their metabolism still functioned. Therefore, the default assumption is that vampires actually dine on some sort of vital energy ties to the blood, the person's soul as it may be.
Dorian Grey, due to his deal with the portrait, has been willfully spoiling his soul, knowing that it will not reflect on his face. Therefore, I suspect that his blood would taste terrible, spoiled. The vampire might gain some small nourishment from it, but I would not be surprised if, trapped within the portrait, his soul's energies are finite, and feeding upon his blood would simply age the portrait faster, having no real effect on the flesh-and-blood Dorian Grey other than to make him that much more callous. And eventually, his blood would carry no soul energy with it.