Not really; a large asteroid is fundamentally incapable of making Earth less hospitable than Mars. For example, it would need to be so large that the impact blew away the entire atmosphere.

It doesn't need to make it just like Mars, to be as inhospitable. An asteroid big enough to crater to the mantle, sending out massive waves of lava and darkening the sky for years would do. It might wipe out all humans on Earth. Of course, unlike Mars, Earth would recover. Not that humanity would care.

> It doesn't need to make it just like Mars, to be as inhospitable. An asteroid big enough to crater to the mantle, sending out massive waves of lava and darkening the sky for years would do.

No, it wouldn't. That would make the Earth much less hospitable than it is now, but still much more hospitable than Mars.

> It might wipe out all humans on Earth.

This is not evidence of being less hospitable than Mars, since humans cannot survive on Mars. Even at the worst point of this disaster, human life would be easier on Earth than on Mars under normal Martian conditions.

> Earth would recover

This concept always feels slightly strange to me. Earth does not "recover" from anything, nor does anything that we or an asteroid could do "damage" Earth. Make it less hospitable for us, sure!

But Earth itself has always been constantly changing due to external and internal forces, sometimes at a rapid rate and always at a slow rate, and none of that change is fundamentally positive or negative to Earth itself.