Unfortunately not. This is because when Spotify syncs it's songs for offline use, it encrypts them in such a way so that only it can play them. This is to prevent piracy (i.e. people syncing songs then either copying them and cancelling their subscription, distributing them publicly etc.). An iPod classic does not support the App Store, so you can't download the Spotify app, meaning there's nothing to decode the music files. iTunes does not have the codecs required to play synced Spotify music (as per my last statement saying it syncs them so that only Spotify can play the files).
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