Yup, the immortality thing comes from VOY "infinite Regress". We only witness it through a malfunction where Seven gets to live the lives of others - we don't know how those ghosts of Drones would experience their own postmortal lives. But the implication is that a Borg never dies.
A different question is whether a Borg gets resurrected into flesh and machinery. The Queen certainly does, repeatedly (and for all we know, she exists in hundreds of bodies simultaneously). Do other Borg? Does Picard also live in the Vinculum, getting printed out in flesh every now and then? Does "Seven of Nine" in fact mean that there are nine physical Annika Hansens out there?
Timo Saloniemi