Not necessarily
I read somewhere that if we bumped up the moon to one Earth atmosphere it would take several thousand years to leach off.
I am not sure how much atmosphere would be created by warming up Mars. I doubt that alone would be enough to make it habitable in any reasonable length of time but it would last a long time in human terms if not cosmic terms.
The reality is, we are probably a lot further away from being able to move or terraform Mars than we are from interstellar flight. We may live elsewhere in this solar system at some point but it will not be in an earthlike environment.