Depends. Are we talking Empire Under the Emperor, or Empire Under Thrawn, or any of the other various times it cropped up?
If the Emperor's Empire, I think it would have eventually imploded on itself and, if it lasted that long, would have been beaten by the Vong (not by much though). Besides, they'd have had at least one Death Star, and would have eventually blown up all the habitable planets.
If we're talking about Thrawn's Empire though, I think he was a vastly better leader and would have been able to hold it all together. Not to mention he'd have made the Vong look like an 8th grader trying to fight Anderson Silva.
Empire under Pruneface.
I doubt they would've destroyed everything... that's just illogical.
Remember, Thrawn became a Grand Admiral in 2 ABY. He definitely had a strong presence in the navy.
The Empire would have lost. They lack the creativity of the former Rebels.
The Death Star might have taken out a few Worldships, but the Vong would have made eliminating that technological "abomination" their top priority.
(says the Rebel scum. Heh heh.
)
I wouldn't say they lacked creativity... Vader became much more mechanical (in thinking and in body), but he was still one of the most creative generals in the Clone Wars.
Regardless, spoken like true rebel scum
I think the Empire would have destroyed the Vong. Not easily, but they would've done it. Then they would've completely eradicated the species itself. No super weapons required, and even without the DS1 they would have had a number of other superweapons at their disposal.
Abeloth would've completely destroyed the Empire, though... it's impossible to tell if she would have escaped in the first place had the Empire maintained its hold, but assuming she did, she would've shredded it and then pissed on the splinters. All the corruption in the government would make the political scene her playground, and I wouldn't be surprised if Pruny made the same mistake as the Lost Tribe and gotten himself killed.
I have no idea how the Chosen One aspect of Vader would help the Empire against Abeloth, but I doubt it would've made a difference.