No, she is not. This might have been hard to understand in the original post since the screenshots are technically out of order, but the Kimono Girls are supposed give the quest reward, not a Nurse Joy. However, if you happen to reach the Glaceon fight, you will get to progress to the Sylveon fight regardless if you win or lose.
In fact, it is probably better to lose because of this. You get "respawn" at the PokeCenter and now your entire team is fully healed, despite having been knocked out by the previous five fights. If you win against the Glaceon, you'll stay in Route 9 and con