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No it is not. The Anime is based off of the games, not the other way around. Anyway, it's probably just a typo when they were selecting the color code for the nurse. Fuschia is the farthest thing from green, so there's no way it could be based off of the town's color.
Perhaps they changed her hair green because everything else in the town was pink and they wanted the player to be able to spot her easily...
The inside of every Pokemon center in the game has a pink floor, so that would raise the question of why every nurse in the game doesn't have green hair. By the way, no nurse in the game has Pink hair, it's clearly orange in Generation II.
Wow I have never noticed that, then again I have not played the GBC games in years mostly due to the fact that my gold and silver both died a few years ago and my Crystal has recently been through it's umpteenth restart. How odd.
Thus it's been years since I have been in Kanto with GSC.