I'm 38.
No, shaving does not damage hair at all. It doesn't change hair at all. Anything about it not growing back, growing back different or growing back thicker is a complete crock.
A lot of my hair is not growing back, but that's because in the years I've had no hair I've been going bald.
Actually, that's been mostly in the last 7 or 8 years. I love it. Easier to keep, and it looks better longer. I am curious as to just what I'd look like if I did grow it out for a few weeks, but not curious enough to do it.
Human hair typically grows from half to three quarters of an inch per month. If you just shaved it off as a one-time thing, you would have what I would call hair in under a week, and a fairly conservative buzz in two weeks. A month to six weeks, and it's long enough to do something with. Shaving your head is not really that much of a long-term commitment, unless you want it to be.
Personally, I think you have to keep your head shaved for at least a month to truly know what baldness is like. Doing it for a day, you're going to have a white, possibly irritated scalp, and your mood is likely to be somewhere between euphoria and embarrassment. It can be a pretty intense rush if baldness has sexual connections or other significance for you. You're going to surprise yourself every time you look in a mirror, and you might initially feel like everybody is staring at you. It might not sound like it, but it's fun. Hell of a rush the first time. Anyway, you need time to get used to your appearance, and for the initial self-consciousness to pass before you can really experience being bald with a clear point of view.
Shaving it once and growing it back is more than most people do, but it's like dipping your feet in the pool.