No. In the gen I games and their remakes, you face Giovanni as the last gym leader, but in the johto region games, he will not be present (save for HG/SS, which has a celebi event in which you can battle him.) in his place, you'll find Blue, the rival from the kanto games and the former kanto champion. In johto, you can battle one of his executives who takes his place while he's training, and he doesn't appear in any of the other regions, since those are the other teams.
