The obento meal ^ is intended to taste exactly how it is out of the box; I think it's the strictest meal choice in terms of how you can tinker with the flavorings using condiments. Soy sauce is the only "extra" provided, iirc.
The sushi in the appetizer portion, if it's a "pressed sushi", is from Osaka and is never eaten with wasabi.
I've gotten cold udon noodles (the white ones) which are served with grated ginger. If it's soba ^ (browns ones from buckwheat), then you get the blob of wasabi as Lori_Q stated.