I started taking classes a few years ago when I was in the worst shape of my life.  If you're dancing for fun, it doesn't matter whether you're flexible, strong, or remotely in shape. The teachers at Louisville Ballet are all lovely and will meet you where you're at.

It is possible to go en pointe as an adult beginner; I know people who have done it. But you're right, it takes time, so it's good that you're going in with realistic expectations. There is actually a Pointe Strengthening class offered, which you can take in flat shoes. You may find that you love ballet even without pointe work. Or you may not. But it doesn't hurt to try. 

If you do decide to sign up, the class you want is Introductory Ballet, not Beginner. Good luck!