While having the moon colonized won't do us much good in the event of an emergency or something catastrophic on the Earth, it will make for a good test run. Our civilization is completely unaware of what it take to fully colonize another planet, but the fact that the moon is easily accessible will give us the opportunity to do a test run. At some point in the future, the things we learned on the moon, will probably be critical to human survival.
Depletion of resources may, at some point, make space colonization an attractive option. Establishing that we can do it on the moon would bolster morale on the issue. However, the moon is not easily habitable. When we speak of colonization, we're looking at planets that naturally can support life such as we know it: air, water, some means of growing food. That's not going to happen on the moon.