First, we know every little about what Morrowind is like now. Aduri implies that Mournhold still stands, and in Lord of Souls we're told the Great Houses still exist (Lord of Souls taking place 20 odd years after the Red year), which means Dunmer culture is still probably intact. Of course, they don't have the Tribunal or the Nerevarine anymore, but theres no indication that the Imperial intituted Kingship in Mournhold has ended, particularly since Morrowind is still an Imperial province.
Second, in order for the Dunmer and Nords to work together, they'd have to set asside thousands of years of hostility and outright warfare. Some Nords can;t even put off preaching about a God they've only had for a few centuries, do you really think they could set asside a hatred that's been engrained in their culture since its beginning?
"The enemy of my enemy, is my friend."
Throughout history, many nations who were bitter rivals, set aside their differences to fight a bigger threat. Just look at WW1 and WW2.
Smart people know what's best for them, and the Empire hasn't really helped Morrowind enough, and with a future war coming against the Thalmor, it doesn't look like anything is going to change soon. Ulfric can offer the Dark Elves a solution that won't rely on the results of a war that hasn't even been fought yet. And there's no guarantee that the Empire will help them even if they do defeat the Thalmor.
If Ulfric is smart, he'd make the alliance happen which would result in the Dark Elves also rebelling against the Empire. The Empire is having a hard enough time defeating Skyrim, so adding another rebellion would surely turn the tides. People say that the Thalmor are trying to divide and conquer, well then it would be smart to ally the rebellion with the neighbors who have similar goals... freedom. From the Dark Elf point of view, the Empire is what got them to where they are, so why should they continue to support them?
A Skyrim-Morrowind Alliance would give both Nords and Dark Elves a chance for freedom. Cyrodil can crumble. Faithless Imperials had their chance to rule, and they failed.
So, will it happen? Who knows? The point is, this enough justification for a Dark Elf to join Ulfric. If that Dark Elf was also the Dragonborn, this would also make it much easier to form such an alliance.