Unfortunately … no. Although Kanto and Johto share an Elite Four and champion (but not conference), they’re considered entirely separate leagues (…partly because of the conference). As such, you must earn a minimum number of badges from the gyms sanctioned for the league you want to challenge.
Of course, you can earn badges within a league in any order you’d like, so if you’d like to earn the traditionally first badge, followed by the seventh, second, sixth, and so forth, you’re absolutely free. It’s just that some gyms are easier to access in a certain order than others.