The F! package is just a CC guarantee, which is different than the pre-pay experiences above. When you get to the restaurant, simply tell them you're on the dining plan (and, they'll likely ask), and you're good to go.
Only the experiences that take full payment in advance matter for that. These are the aforementioned CRT and the dinner shows. Any restaurant/experience that simply takes a CC guarantee (F!, CG, Akershus) won't matter one way or the other.