I agree going to Mars is never going to be a useful for evacuation, but it could help if we where already there.

Most plausibility the long duration space flight should prevent the common cold from making the trip which would also prevent many hypothetical super plagues from doing so as well. In theory you could do the same on earth, but it’s unlikely for a self sustaining underground colony to consistently maintain that level of quarantine for new arrivals.

However getting a self sustaining population on Mars that could survive indefinitely is currently just science fiction and making the trip is the least difficult hurdle for changing this.

To be clear, off-planet colonization isn't an evacuation strategy. It's a continuation strategy in the event that humanity is wiped off the Earth.

Earth obliteration is a certainty on a long enough timeline, before the Sun goes out. There's no question of riding things out underground at that point. We'd have to be elsewhere.

You'd probably live underground if on mars anyway.