Life is exceedingly adaptable and very hard to extirpate. It probably existed already at the dawn of Universe, even technically advanced life (Przybylski’s star and Barbenheimer star might be ancient nuclear waste dumps). So the answer, imho, is positive. The main great protector of life in the Solar System is actually not Moon, but Jupiter. Not only it acts as a cosmic Dyson vacuum cleaner, capturing and rerouting comets and even small asteroids, but also influences Earth’s long-term orbital cycles greatly. My longread dedicated to said phenomenon can be found here, though in Russian.

Also see Seveneves by Neal Stephenson, where humankind needs to survive after the Agent of unknown nature, probably wandering microsized black hole, shattered Moon apart. Spoiler: it succeeds, though only barely — because of exceptional hubris & stupidity of person who’s equivalent to Hillary Clinton in the world of novel. This work by Stephenson predates Don’t Look Up by some years, though alas it’s not so widely known. I say alas due to slightly absurd, but definitely optimistic, feeling it induces, unlike Don’t Look Up.