You can actually sit through recap videos in the beginning if you want. They are quite lengthy so... grab some popcorn and beer if you are going to watch it.

Yea there are recap videos at the beginning, but it's a pretty lengthy story.

I did this with the third one and was fine.  I never played either of the first two and when I started playing 3, I sat through the recap videos and was fine.  To be honest though, even people who have played the earlier games get lost from time to time.  The game is completely in Japanese with subtitles so it's easy to get confused with people's names, locations, etc.  This isn't a knock at the game, it's amazing, but it's ok to be confused and/or lost...it all comes together in the end.

The plot? 
 
You will probably understand it as much as any japanese video game with a story, that is to say; not at all.