Are classes and other material from Unearthed Arcana articles legal to use in Adventurers League, or are they a kind of beta phase intended for playtest only before they go official?
Unearthed Arcana articles
The content of the Unearthed Arcana are designed partially for play-testing ideas and seeing where the fans are focused in class, race, and option design. They are all optional content that is designed for WOTC to perform surveys on, improve, and refine before a possible release either as a later form of Unearthed Arcana, or in books to be later sold. An Eberron source book has been hinted at by the direction of the First Unearthed Arcana entry and other information, but they are very vague hints and nothing concrete about their plans are known yet.
Adventurer's League characters
The documentation for the Adventurer's League is very specific about what content can be included in the character creation process, and for many reasons. Even within larger bodies of contents, such as the Elemental Evil Player's Guide, individual options may not be available to players. The Aaracockra is an example of this. Every season will have its own options available to players. These options will always include the Player's Handbook, and will generally include a Player's Guide for the season if one has been printed. Even class options from the Dungeon Master's Guide are generally not allowed (with very limited exceptions based on certs offered at conventions).
What this means
The bad thing about this is that no characters outside those that are discussed in the Adventure League Player's Guide is available for play in the Adventure League, and even within the sources that it allows you to use, you are restricted on combining options. It's not so much about unofficial versus official, as what they are allowing in an organized setting specifically.
As an example of restrictions placed, the Sword Coast Adventurer's Guide is allowable for all story lines, but can not be used in conjunction with the Elemental Evil Player's Guide, even if the character is from the Elemental Evil story arc.
Currently there are no Unearthed Arcana entries even mentioned in the AL Player's Guide, so you cannot use the options presented within any of them. It is highly unlikely that any Unearthed Arcana entries will ever be present in AL, since they are considered to be in draft form. When the options are refined (assuming they are not scrapped), they will become available through official releases such as the Elemental Evil Player's Guide and the Sword Coast Adventurer's Guide.
Since June '15's "Variant Rules" Unearthed Arcana, each entry has been introduced with this disclaimer:
You can think of the material presented in this series as similar to the first wave of the fifth edition playtest. These game mechanics are in draft form, usable in your campaign but not fully tempered by playtests and design iterations. They are highly volatile and might be unstable; if you use them, be ready to rule on any issues that come up. They’re written in pencil, not ink. For these reasons, material in this column is not legal in D&D Organized Play events.
I believe this text has been retroactively added to earlier entries in the column, but maybe it was there all along.
D&D Organized Play includes the Adventurer's League, so no, you can't use Unearthed Arcana material in Adventurer's League events.
Some of the articles have proven to be "a kind of beta phase intended for playtest." The Sword Coast Adventurer's Guide included revised versions of material that had previously appeared in Unearthed Arcana: Waterborne Adventurers, the Swashbuckler roguish archetype and the Storm Sorcerer sorcerous origin.
The class versions presented in this particular Unearthed Arcana are essentially house rules that they've published to give you some examples of what using the DMG's house rule construction advice should look like.
They are not presented as Beta material (like the Eberon and mass combat rules were). They are presented more as examples to support an explanation of design intent. Other issues of Unearthed Arcana (like the ones mentioned above) are presenting prospective rules material for playtest, that does not seem to be the case here.
I would not expect these examples to ever become legal for Adventurer's league play. That said, I would not rule the possibility of these subclasses being published completely out. But that does not seem to be the intent of this presentation.