If Earth were hit by a dinosaur killing asteroid it would be more habitable than mars before, during, and after.
Any ridiculous boondoggle might have beneficial side effects. There’s no evidence, however, that spending money on a boondoggle is a more effective way of generating positive side effects than spending the same money on something sensible.
I contend that if we were to spend $400B on a crash program to cure cancer we might accidentally end up figuring out how to live safely on mars.