Not exactly. Presumably almost all imperfect replications lead to dead ends (or we'd all be dead). Also, because they transmit poorly from host to host, even if one did evolve, which might be impossible, it'd probably die when it's host did.

Given that each human replicates each protein many millions of times over the course of their life, and that there have been several billion humans alive, if that were possible we'd probably have experienced it by now and again all be dead.