I'm trying to avoid Akonadi, mostly because I haven't had much success with it (e.g. with syncing gcal in KOrganizer). I notice that Kopete seems to require it. (I'm using Kopete for Windows Live Messenger, Google chat, and Facebook chat via Jabber & XMPP.) Is there any way to get Kopete to work without relying on Akonadi?

Kopete uses the KDE PIM contacts infrastructure, which means that at this time, it is dependent upon Akonadi also. Unfortunately I do not believe it is possible to not use Akonadi with it.

Are there any benefits of it using that infrastructure? Can it sync with my contacts KAddressBook or anything?

Your contacts, once in Akonadi will be accessible by all Akonadi enabled applications, including KMail and KAddressBook. I am not sure to what extent or how Kopete integrates online server contact lists though.