I can confirm it works. Just download the app onto your v1, sync and the app will appear in your iTunes. Then when you upgrade to the 3G, do a restore from back up and the 3G has everything your v1 had. It was a really easy and pain free process going from the v1 to the 3G. Just takes a while!
the app is locked to the iTunes account of the person who purchased it, not the iPhone, or computrer it was purchased on. So, if you hook up multiple iPhones t the same computer, as long as they are authorized, you can put it on other iPhones, 3g or not.