I was given a Tile as a gift at some point, but I can't seem to locate it at the moment (irony!).

Since there's nowhere on the Kobo to attach the keychain variety, I'm assuming you'd be using the sticker kind? It should probably work, although depending on whether you put it on the front or the back of the case, it may mean that the Kobo no longer lays flat on a table.

I would be concerned if there were magnets on the Tile, as this could interfere with the Kobo's ability to properly detect the Sleep Cover, but it doesn't look like there are. It's all over Bluetooth.

Since there probably aren't too many Kobo owners with Tiles on them, my suggestion would be to google around for Tile + Kindle, to see how people have reported their experiences with the two. Any shortcomings people notice with a Tile on a Kindle/Kindle Case would probably match pretty closely to a Kobo, given that they're similar devices with similar dimensions.