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.

If the spell required you to share a language with the creature, it would say so.

Let's look at something like Modify Memory (PHB, page 261)

You must speak to the target to describe how it's memories are affected, and it must be able to understand your language for the modified memories to take root.

It's specifically called out that the target must be able to understand your language.
Command (PHB, page 223) is another example:

The spell has no effect if the target is undead, if it doesn’t understand your language, or if your command is directly harmful to it.

Since there is no mention of language in Conjure X's description, it will follow your commands regardless of the language you speak them in (although I think it would be a reasonable assumption that it has to be a known language within the DnD universe, not just one you made up on the spot).

Note though that the spell only says

they obey any verbal commands that you issue to them.

It doesn't allow you to automatically understand the creature's language, give the creature the ability to actually understand your language (unlike the Find Steed spell), or give it any special ability to communicate with you.
As per @SevenSidedDie's comment, they may not even understand the actual commands, being driven more so by magical impulse at the intent behind your words rather than by the words themselves.