For life as we know it to continue it would have to be a small asteroid. Yes it could happen, and such a scenario would be greatly preferable to one impacting the Earth. The Moon too might one day capture an asteroid, and indeed there are asteroids with smaller orbiting asteroids out there in the depths of the solar system.
Most asteroids are tiny compared to the Earth (see Wikipedia) and the large ones capable of disrupting the Earth's orbit seem to be very unlikely to approach closely enough to be captured as a satellite. However, as you imply, we can't be absolutely sure a very massive rogue body exists, which may one day be captured in Earth orbit, disrupting evolution and causing many extinctions including mankind. Even so, unless the body is truly massive, say a tenth the mass of the Moon, persistent life would carry on, perhaps the only survivors being very small land and sea creatures, and of course almost indestructible bacteria; and evolution would continue relentlessly with new adaptations.