Yes it does
Yes, you can add beast forms to your Wild Shape repertoire of beasts seen by casting conjure animals. The spell explicitly says the conjured creatures literally are beasts, and a creature of the type beast is all Wild Shape needs you to see in order to add its form to your repertoire.
Though someone might by tempted to quibble that they're not real beasts because they're really fey spirits clothed in the shape of beasts, look at it this way: First the Druid conjures a bunch of spirits that take on the form and behaviour of the real beasts they look like. The creatures so conjured proceed to behave and look exactly like the real thing. What better opportunity is there for a shapechanger to learn a new form to wear, than to see a nature spirit do the exact same thing as they're wanting to learn to do?
But it's of limited use
What you might actually run afoul of is limitations on metagaming, or a DM whose setting doesn't include just any creature you can think of (even if it's in the Monster Manual).
- A DM who wants to limit metagaming would be within their rights to ask you to justify your choice. If you try to summon a Giant Owl but your druid has never seen one before, a DM could easily say "How do you know those exist? You've never seen one. How is your druid "choosing" an animal (s)he has never seen or heard of before?"
- A DM who has developed a custom setting isn't straightjacketed by the Monster Manual and doesn't have to include everything in it. Giant Owls might not exist in a DM's campaign.
This also means that this is much less of a loophole than it might seem — after all, how big is the difference between the set of creatures a druid has personally seen and the set of creatures the druid knows about well enough to deliberately try to conjure? I can't imagine it's a very large number.
But in principle, yes, a conjured animal inhabited by a fey spirit is plenty to learn that form from. Just mind that, if you can conjure a particular animal, it's highly likely your druid has already seen it anyway. This makes this method of acquiring new forms both limited in utility and not much of a loophole to worry about, either way.
The key word here is indeed beast.
Beast is a defined type of creature within the game, as per page 6 of the Monster Manual;
Beasts are nonhumanoid creatures that are a natural part of the fantasy ecology. Some of them have magical powers, but most are unintelligent and lack any society or language. Beasts include all varieties of ordinary animals, dinosaurs, and giant versions of animals.
Since Wild Shape specifically says
assume the shape of a beast
you are limited to only creatures that have the beast type.
Note that at level 10 a druid of the Circle of the Moon gains the ability to Wild Shape into an air, earth, fire, or water elemental, but it specifically limits it to those 4. This does not allow the druid to Wild Shape into any creature with the Elemental type (such as a Galeb Duhr or Gargoyle).
Best Answer
There are no official answers from the adventurer's league at this time. However, I think we can apply some rational thought and come up with a good answer in the meantime.
All Adventurer's league PCs start out at L1s, Wild Shape is a L2 ability, so I would track what you've seen while adventuring. You might be able to make a case from your background of what you've seen prior to your adventuring career, but it might be a hard sell to an organized play DM.
I would definitely do this. At the very least for the ones that don't show up in the PHB that you'll encounter. I doubt you'd be called on it, but it wouldn't hurt to have a menu.
For beasts that are not in the PHB (I'm not sure there are any right now, but just in case), you've got some options. Between the BD&D DM book, and the HotDQ online supplement, you can easily find any beasts that might show up in the current season of organized play that are not in the PHB (and going forward, they plan to release similar supplements for future adventures to keep BD&D the only required materials). Everything in those two online supplements will also be in the Monster Manual that is coming out at the end of September.
Ultimately, I don't think this is something to get too hung up on. I find it improbable that you wouldn't be able to make the case to even an Org Play GM that you hadn't encountered a certain beast before. I'll note that even org play GMs are given this kind of latitude in the instructions to them. However, I also wouldn't make a big stink about it if the DM said "no, you can't be a Stirge, you haven't seen one of those yet" if you don't have it written down that you'd encountered one.
I reached out the D&D adventurer's league on twitter to get something slightly more definitive and here's the response:
So the official response is "whatever you think makes sense for your character", that's pretty much in keeping with the spirit of 5e's rulings so far and makes sense. Again they've given 5e org play GMs (and players tbh) wide latitude on stuff like this, so decide something that makes sense with your characters background and story.