First, a few key elements of that trilogy were contradicted by the prequels, essentially the pre-OT back story elements in there (the clones in Zahn were not the stormtroopers, notably). One notable exception is the capital planet Coruscant. I don't know if it's ever been established that Lucas gave Zahn the name or not, but the concept of the city-planet comes from Lucas' early drafts, when he had not yet decided to focus on Luke. Some, a lot, of the set up/universe Zahn's trilogy would be totally irrelevant 30 years ahead, other things however would tie their hands.

While they might pick some elements in there or recycle a few of the EU's better ideas, their "main cast" for the new movie doesn't make it very likely (eg: there's no woman cast who could be Luke's EU wife, there's a serious lack of older figures to play some big EU characters). The trilogy would really bind their hands concerning characters and relationships, as it introduces as a central player Luke's future wife as a Jedi-to-be (working for the villains, at first), establishes the unborn Solo twins and the Han-Leia wedding, etc. Most of all, it's a story about a half-mad "Dark Jedi", a concept that Lucas hated (in his mind, for the movies, only Sith and Jedi should exist. Someone who uses the Dark Side is a Sith. Lucas erased that Zahn villain from the prequel era altogether. The "only 2 Siths" rule was also a new concept introduced only by Lucas's prequels, like also the symbiotic relationship between tiny things and the Force). Beside, the trilogy shows the last days of the Empire almost directly after ROTJ and would bind their hands to that course of events for the political background, and I'm not so sure it's where they want to go (by 30 post ROTJ, the Republic and Jedi Order are pretty much back in place, the EU had been running in circles for a while and its managers decided to reshuffle the cards by having a huge invasion of silly insectoid aliens from another galaxy and immune to the Force come to destroy a lot of it...)

From there it only gets worse, as the characters and events/concepts created by Zhan were highly influential and came to take the center stage in future EU books. EU writers have mined some of its elements for years. I don't think it would be too great an idea for them to borrow characters or names and give them a complete make-over, that will only make the EU fans more furious (they can get quite rabid, as anyone who's followed the SW boards during the production of the prequels will remember. They went mad at Lucas at every little new contradiction of the EU.. .which is why I think it was a wise decision to push their sand box completely away and officially: the movies will no longer contradict the books as they are no longer the real canon).

Nothing prevents them from mining a few EU ideas, a bit like Lucas himself did in a minor way (a few names, a background bounty hunter whose design he really liked etc.), but my guess is that they won't do it much. I wouldn't be surprised that much like Lucas himself for the prequels, Kasdan and co. have not even read the EU and more or less ignored it completely. At first they didn't even know for sure they'd have Carrie, Mark and Harrison, nor to what extent. They are, or were, fairly prominent figures in the EU. It's also established that Leia doesn't train her abilities, and I'm not quite sure they'll go there in the movies, when a lot of the movie fans expect them to follow up on "there is another". Zhan had captured more or less the spirit of Lucas's storytelling/mood, but more and more the EU has strayed from that over the years to get in seriously un-Lucas territory, and I think it's a major reason why they won't be keen to borrow from it if they want the movies to remain true/in the spirit of George Lucas.

That said, some "EU concepts" are so obvious that a variant on them is very likely to show up... unless they go elsewhere. That might include the fact that Luke has become the mentor to a reborn Jedi Order, and the fact Leia's the main politician in the Republic... if post ROTJ the Republic has been recreated... The Old One was flawed and deeply so - way too big, way too corrupted, and as the EU was not drawing until late on Lucas's real story of the pre-Empire downfall of the Republic, its problems, its factions, the EU's vision of the post-ROTJ politics isn't exactly what'd you expect either. The sequels could very well introduce a galaxy with many competing factions, instead of a new unified Republic. There could well still be remnants of the Empire, or old Empire era renegades..a kind of Tarkin-like figure, like in Zahn, but 30 years later. It thought immediately of that upon seeing von Sydow.

And there is a big "but": Lucas's own vague concepts for the sequels have very likely been taken into account, and from the little we know about them, validating much of the pre-ST EU background won't do. For Lucas it was to be the "philosophical" trilogy, after the political one and the swashbuckling one. I suspect personally that Luke won't really have recreated the Jedi Order as the trilogy opens, and it's not quite impossible that the Republic of the prequels has never been recreated. I also suspect Luke won't be a father and husband but will have turned himself into another OT Obi-Wan on his way to a Yoda figure, and maybe shown as quite reluctant to take on apprentices. Fisher and Ford OTOH may well have had kids who will be among the leads but I doubt they'll owe much to their EU counterparts.

I also have the suspicion they intend to kill one of the original characters in the first movie, quite possibly Luke.

Also: can they have a new trilogy without Sith Lords vs. Jedi duels? I don't know... Can they have some without repeating the whole "fall to the dark side" of a Jedi story line? I guess it would be possible.. eg: untrained force users recreate the Sith Order, or something like it, while Luke hasn't recreated the Jedi and now must, but we'll see. SW movies without the iconic lightsabers duels would sure be strange, but the "good character falls the the Dark Side" idea is pretty much dry at this point.