Correct
If the transplanted hair comes from a region where the hair doesn't fall out, then even after moving it, it still won't fall out. Those follicles are immune to DHT miniaturistaion. Hair does naturally thin with age though, as the telomeres are worn away through repeated cell replication and the genes are eroded. This isn't male pattern baldness though, this is just something that happens to every living mammal.
Any hair that remains on top that wasn't transplanted from the back and sides can still fall out.