Well, it could happen that way, but it doesn't have to... so it makes sense to check before deciding that just because you logged in in its embedded browser, that the OverDrive Account was linked to your library logins.
IIRC, when you sync the app to a new device, your known libraries are preserved, I do know for a fact though that you will have to re-login to each account. I assume it is saved as a browser cookie, and those aren't synced.
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