I mean, without heart, nothing can grow. Can we human live without heart, and really without heart lol, this is not sarcastic, NO.
Can Nobodys live without heart? Yes they can, thats their special thing, but, without the main thing of her body, nothing is possible..
You're forgetting that the soul is still there. Without the soul + body, um...ded. If you're not dead, I imagine you're still aging, and Namine and possibly Xemnas definitely reflect this.
What IS the heart, though? The conscious self, evidently, complete with all the original self's memories. Roxas running around without Sora meant that he didn't have Sora's consciousness (or at least not totally), but he was still alive because he still had that soul there. (Maybe the soul is the Nobody's consciousness, as in an adaptation in lieu of the Somebody.)
So I really don't see how the heart is connected to aging. If anything, it's the body. You could say that a person matures--through hormones (connected with the body).
For example, Sora didn't age, if you really think about it--not psychologically. When he popped out of the pod in the beginning of KH2, he had the same mentality of young Sora who got in there originally. (That is, until the hormones kicked in and he started going around playing matchmaker to everyone in Disney.)