There are three distinct products we are talking about here when it comes to any of these settings-- an adventure path book, an adventurer's guide, and a campaign setting book. Each one has a different likelihood of showing up in the near-term, long-term, or not-at-all-term.
If we're asking "Will there be an Eberron-located adventure path book"... I would guess the odds are good that it will indeed occur. However, probably not until two or three adventure path books down the line.
If we're asking "Will there be a Five Nations Adventurer's Guide"... my guess would be that it's probably unlikely any time soon.
If we're asking "Will there be a 5E Eberron Campaign Setting" book... my guess is nope, not happening.
If I were to guess what we'd most likely get... I would tend to believe it'll depend entirely on the form and function of this supposed "big new mechanical book" that has been offered forth. If WotC is going to produce this "Player's Handbook II" or however you want to identify it... it seems to me that that would be a pretty good book to put all of the "specialty" character stuff from all of the various campaign settings out there. Basically, rather than publishing six different and separate "Adventurer's Guides" for Greyhawk, Dragonlance, Eberron, Dark Sun, Planescape, and Mystara to cover all their individual character creation needs (and needing like 7 years to do them all)... they instead give each of them individual chapters in this "big book o' mechanics", detailing everything there instead. Backgrounds, unique races, unique classes, special abilities (like dragonmarks), unique mechanics (like defiling) etc. Then on top of that you add some of the bigger new mechanical stuff like psionics and the Mystic... and you get to nail seven birds with one stone. Then after you release that book and get all the individual settings up-to-speed mechanically... you can then start dropping in individual Adventure Path books from the different settings as needed/wanted.
I have no idea if that's what they are going to do... but I have to think that if they *are* going to produce another big book of character mechanics to rival the PH... deliberately *not* including the character mechanics needed for the various settings that need them seems to be a waste of potential. Why produce this giant book, only to then need to release an adventure's guide two years later for Eberron to cover the mechanics for dragonmarks or the artificer? Wasting paper if you ask me. Just put the artificer in the big new book and get it taken care of rather than needing to hold off.
But of course the most important point in all of this is that No... they are never going to do a 5E version of the Eberron Campaign Setting book because literally NOTHING has changed story-wise that we don't already have printed in the 3.5 and 4E versions. There's absolutely no reason for them to re-write two entire books of the exact same information just so they can print them with the 5E logo on them. Not happening. You want the Eberron fluff... head over to DMsGuild and buy the campaign setting book PDFs.