The words may be etymologically related. The word kaveri has two suggested etymologies; the first is that it's originally a variation of toveri (which is more formal; also means "friend", but has a leftist connotation, like "comrade"). The latter is fairly straightforward loan from the Russian товарищ (tovarištš), which is probably closely related to the Bulgarian aver. Interestingly, the ka- in kaveri may originate from the Swedish kamrat, quite clearly related to the English "comrade".
The other hypothesis is that kaveri is from the Yiddish חבֿר (khaver), which is a direct loan from Hebrew.