In Part 1, she was able to throw off/recognize genjutsu. Maybe that's why she's a 'genjutsu type' ? Otherwise, I've never seen her use it in the manga/anime...As you said OP, Kakashi stated at the beginning of shippuden that sakura could surpass Tsunade because she was a "Genjutsu type"
I would assume that this means she would have to be able to use genjutsu at that time.
Also, if you're counting games, I believe she was able to use Genjutsu in several of the games.
The games wouldn't really count since their not part of the story-line...
Still, I guess I wouldn't be surprised if she ever learned.
But not now, during the war. 0.o