I wasn't able to find any integration with overdrive in Canada when I last tried the kindle. The Kobo's here do work seamlessly with overdrive but only for ebooks though, no magazines or audiobooks
An alternative is to use the Libby App on the phone. You can also download the magazines for offline reading.
Or you could use the Libbyapp [1] on the browser to sign in to your Overdrive account, borrow and read the magazines.
With that being said, it would be amazing if Kobo can implement support for magazines so that you could use eink displays for reading magazines in a park on a sunny day without any glare
That should work on a Kobo. But it requires Overdrive to recognize this and push the readable formatted magazine to the Kobo.