Yes but in their US integration, it's actually a bit more glitchy than Kindle especially if you're juggling multiple library cards. You can still make it work, and I do bother with that because my Kobo is such a better device than my Kindle, but it's more of a headache than using Libby to send to Kindle.
Kobo is owned by Rakuten who used to own Overdrive/Libby.
yep, that's exactly why I got a Kobo, so much better
Kindle does this too via Libby.
Only in the U.S.
Is Libby available elsewhere?
Yes. Overdrive and Libby are available elsewhere.
I'm using a library card outside of the U.S. with Libby and send all my loans to my Kindle via amazon.de, works fine
Is it a U.S library card? Or a library card from outside the U.S (e.g., a German one)? That's not clear from how you wrote it. I believe it's a U.S library only thing. Libby's own FAQ says it's U.S only but perhaps they just haven't updated it.