Ideally, an enclosure for a low frequency driver does not vibrate at all. Some people go so far as to make the enclosure from poured concrete, but usually at least 3/4" MDF or Baltic Birch plywood is used (often with double thickness for the baffle) combined with internal bracing to minimize enclosure resonance. Vibrations from the enclosure "color" the sound, which is not a good thing.
So, it depends on how well the "bass box" was built. If it was built cheaply, it will probably vibrate a good deal. I wouldn't worry about distorting the sound. The only sound you would be changing by standing on a speaker box is the sound from the box resonance itself, which is undesirable in the first place. Standing on it would deaden the vibrations to a degree, which should/could be a good thing in terms of sound quality.