It depends. If all she is interested in is free roaming as an 18th century pirate, then no. But if she really wants to get into the story, history, lore, etc, then I would highly recommend looking into the other games before playing Black Flag, because without doing so she'll be lost during the 2012 missions.
The first three can be found for under $10, and the last two no more than $20-$30 at this point. The reason I say so is because the game tells a simultaneous story - it's basis is upon a person in the present day using a device that allows him to relive the memories of his ancestors, the assassins.
The whole purpose of this was the idea of the world ending in 2012, and it becomes a race against time to search through his ancestors DNA and memories for clues as to how the impending doom can be stopped. While the historical stories following the assassins are good and interesting in their own way, the current day storyline is actually the central focus and the one story that continues from one game to the next.
Technically, if she wanted to play through all of the games she could as long as she just focuses on the main storyline. These games are pack with side quests which can extend gameplay another 20-30 hours; the main story itself shouldn't take longer than 10-12 at most in each game. If she goes this route, that's plenty of time to finish before AC4 releases. My girlfriend is doing the same thing right now - she recently finished the first game and is a little over halfway through AC2 at this point. Worst case scenario, I would at the very least go to YouTube and watch the important story moments from each of the previous five games.
