Note that the Yuuzahn Vong are entirely part of the non-canon Legends continuity; they do not exist in the new canon. So in the "main canon", the answer is clearly no: Palpatine did not anticipate the Yuuzahn Vong, because the Yuuzahn Vong do not exist<sup>1</sup>.

In Legends, the answer is

Probably, partially
---
The novel *Outbound Flight* reveals that, at least as early as 27 BBY, Palpatine was aware of a threat of invasion from a group referred to as the "Far Outsiders":

>"There's an invasion coming," he said. "A massive assault force of dark ships, shadowy figures, and weapons of great power, based on organic technology of a sort we've never seen before. We believe these Far Outsiders, as we call them, already have a foothold at the far edge of the galaxy, and even now have scouting parties seeking information on worlds and peoples to conquer."

>*[...]*

>"When will Darth Sidious tell [the Republic]?"

>"When he's turned the Republic's chaos into order," Doriana said. "When we've built an army and a fleet capable of dealing with the threat. To announce it before then would do nothing but create panic and leave us open to disaster."

><sup>*Outbound Flight* Chapter 18</sup>

The Far Outsiders sound very much like the Vong we meet later, but they're confirmed as one and the same through Vergere, who's said in *Rogue Planet* to have left Zonama Sekot with the Outsiders:

>"We came here to buy a ship from you, and to find out what happened to Vergere."

>Shappa chuckled grimly. "It's all tangled, isn't it? She's gone."

>"Where did she go?"

>"She left with the Far Outsiders."

><sup>*Rogue Planet* Chapter 45</sup>

She turns up again in the *New Jedi Order* series as a servant of the Yuuzhan Vong.

Although we don't have confirmation that the Death Star was itself intended to be used against the Vong, we know that Palpatine was:

 - Aware of the imminent threat of invasion
 - Building a unified Empire for the purpose (at least in part) of repelling that invasion

Which seems to pretty strongly suggest that the Death Star was a tool for use against the Vong, even if only indirectly.

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<sup>1</sup> At time of writing, anyway; the Lucasfilm Story Group hasn't shied away from borrowing [popular EU elements][1] for new canon works, so you never know how things might change in the future. And note that some newer canon novels (*Empire's End*, *Thrawn*) indicate that Palpatine *was* concerned about threats in Dark Space, and that the Chiss Ascendancy was monitoring hostile *somethings* out there, so it's not impossible that we could see the Vong return to canon


  [1]: http://www.starwars.com/databank/grand-admiral-thrawn