I was going to call this an "update" but realized that might be misconstrued to imply that there was a new Alpha (or even a Beta) build up.
In terms of Blizzard's promise that the Legion beta would begin before the end of 2015, I would say they kinda-sorta delivered. They half-delivered, given that Alpha is the first letter of the greek alphabet and Beta is the second. So, half of two is one.
Still, what's up looks pretty good. We've seen a good portion of the specs playable there, and the Alpha was extended beyond the usual Friends-and-Family to various games journalists. As far as I know the general public hasn't gotten any invites, but it's still much more (intentionally) public than other Alphas have been.
I suspect that by the time they turn it into a true Beta, with random schmoes like you or me logging on, we might see a far more complete build than we've seen in previous tests. Recall, for instance, that when the Warlords beta launched, only Shadowmoon and Frostfire were open for testing, whereas they're already in that state now, plus two dungeons are open for testing as well, not to mention the many artifact scenarios that are open along with several class halls, and so presumably the beta will have more parts opened up.
Blizzard gave themselves the deadline of September 21st as the latest time for release, but you'll note that that's the first day of fall, which implies that the release is slated for summer of '16. That could, technically speaking, come as early as June 21st.
The question, then, is whether it could come in the spring.
Blizzard is clearly not holding themselves to such a release. I think the real question is how much this "Alpha" can count against the time required for a rigorous Beta test. As far as I understand, the questing in both Stormheim and Highmountain is entirely open for testing, and while there are a couple of placeholder models, and they might decide they need to go back and redesign some things, it's possible that they're more in the "sift through for bugs" type of testing there.
I believe previous tests have taken 4-5 months, but again, we have to wonder how much this "Alpha" will count against that time. Obviously, we shouldn't consider these durations hard and fast rules, but they might be a good indicator of what to expect.
In terms of player goodwill, getting Legion out asap would be in their best interests. The "shorter expansion" model only works if that final raid tier really doesn't stretch out too much. In order to simply match the usual period of "final tier" to next expansion, they need to release around June. But in order to justify the truncated Warlords expansion, they need to push it up even further, because otherwise this simply means that shorter expansions mean proportionally more time spent in the end-of-expansion doldrums.
Testing and implementing new content can be very unpredictable from our perspective, but given what I've seen them come out with before this holiday break they're taking (and I certainly won't begrudge them a little break for the holidays,) I think it's possible for them to release earlier than the summer. How much earlier? Well, I'd still wager that it's not going to be until late spring. If we assume that the test goes into full-on beta mode when they're back from the break, and that we even count the previous Alpha testing as equivalent to a month of beta testing, that still means that we probably wouldn't see a release until late April.
That said, if they could pull it off, I would be pretty happy with an April or May release. But we'll really need to keep a close eye on the progress over the next few months. If they have all the zones open for testing before the end of January, that'll bode well. But even then, there can always be big hurdles to jump. Legion is not only adding a new class, but also a fairly complex new artifact system, plus a PvP talent system, and so there will probably be a whole lot of effort required to balance all of these things out. Not to mention the level-scaling zones.